A CNC is simply a machine which controlled by a computer to perform a repetitive or accurate task otherwise not possible or cost effective by hand. The basics are true for all machines, whether it's a robotic arm painting cars on an assembly line or a flatbed router cutting plywood: a series of commands are sent to a controller which drives a motor which moves the machine. The following information is focus on the flatbed cutting machines which are usually routers, plasma, or laser cutters.
The three axis flatbed CNC (I'll just refer to it as a CNC beyond this point) is essentially a table with a cutter positioned over it. The cutter is able to move left and right and back and forth across the table. This will be the 'X' axis and the 'Y' axis and will depend on the manufacturer on which is which. The cutter will move up and down, the 'Z' axis. There will be variations to this, such as an addition cutter head or a cutter head which rotates away from a vertical position, and these additional items will receive axis identifiers. But the basic three axes are two in plane with the table and one perpendicular to it.
Each axis will be driven by a special motor. This motor is capable of accurate rotation; it is possible to control the position and the speed of rotation. This will require a special motor controlling system, and there is more information about that further on. The computer in the equation is used to transmit the motion commands to the controlling system and to provide a human interface with the machine. Finally, there is usually a second computer used by the designer and it the source of the motion command file.
The scenario is usually like this: The designer wants a shape cut, or 1000 of the same shape cut, and a cutting file is created. This file is sent to the computer connected to the CNC. The CNC operator loads the file into the CNC control software and initiates the file. Each line of this file is something like 'move cutter to here', 'move cutter down', 'move cutter to here and here and here', 'move cutter up'. These commands are interpreted by the controlling system to 'spin this motor at this rate, in this direction, and this many times'. The CNC then operates in a controlled fashion.
It is not necessary to understand the details involved with the operation of a CNC machine. The following information will touch on these details, but only to the point where it benefits someone interested in selecting a new machine. The goal of this writing is to provide insight into specific differences between similar machines as an aid for comparison.
MATERIAL TO BE CUT
A typical flatbed CNC will be used as a router to cut plywood, foam, or plastic sheet or as a plasma/laser cutter for steel or aluminum plate. On occasion, you will find one that uses a special cutter or marker for fabric, paper, or thin plastic sheet. Each will have its own specific requirements. So not all CNC's do all things well. For instance, it is possible to put a plasma cutter on a router style CNC, and many people do just that. But a CNC set up specifically for a plasma cutter will have a water table below to catch the sparks and slag, a spoil support to protect the table, and a table designed for the unique weight and size of metal plate (which is not always 4' x 8' and will likely weigh several hundred pounds). Therefore, it is obvious that the machine to select will be designed for the material that will be cut.
In most cases the cutter will be mounted on a head which is suspended above the table on a gantry. The head is able to move left and right along the gantry and is able to move the cutter up and down. At this point, flatbed CNC's fall into two categories for motion in the remaining axis: moving gantry style and moving table style.
A moving table style will have a fixed gantry and the table will move back and forth. The primary benefit of this is that the gantry can be built very stout (and likely weigh more than the moving table). A stout gantry is desirable when multiple cutting heads are mounted or a large clearance is necessary which translates to higher twisting moments on the gantry.
A moving gantry style will have a fixed table with a gantry that rides down along the table on rails. This design uses less floor space since clearance is not required for a moving table. Additionally, this simplifies vacuum hold down piping requirements.
Why the difference and which is better? It boils down to which is heavier and harder to move, the gantry loaded with spindles and tools, or the table loaded with material. The heavier one gets fixed.
LINEAR MOTION TRACK, SCREWS, and MOTORS
Once you have a table and something that moves around to cut the material, you need something that actually does the moving. A motor with a rotary motion must be converted to a linear motion and this is done with one of two systems: by screw drive or by gear and track. Each manufacturer will tout that whatever system they have installed is best, but they both have their pros and cons.
A screw drive (ball screw, Acme treads, etc.) makes for what appears to be an easy installation. The motor at the end of a fixed screw rotates the screw to move a nut. The nut is attached to the thing that moves. Each rotation of the screw moves the item only a fraction of an inch so a gear reduction isn't needed. Easy. However, the nut on the screw has some looseness to it so when you stop and try to go the other direction, there is a period of which the nut doesn't move until it contacts the other side of the screw threads (this is called backlash). So the nut needs an anti-backlash device which complicates things. The screw also needs bearings and devices to allow it to rotate but hold it in place and this complicates things. And one final limitation is the length of the screw. If you plan on a 16' long table, odds are it won't be driven by a screw.
A gear and track drive also appears to be an easy installation. A toothed track runs the entire length of the path to travel and a motor with a toothed gear fits into that track. The motor is attached to the thing that moves. Also easy. However, the force from the motor which pushes the item down the track also tries to push the gear out of the track. Each rotation of the motor moves the item several inches, depending of the diameter of the gear, and this necessitates a gear reduction or a large motor with a micro-stepping drive to provide the torque and resolution required.
Servo Motors vs. Stepper Motors... that's one of the biggest battles out there. A few decades ago, stepper motors and drives were only commonly available in smaller sizes. Servo motors (which are just DC motors with a location encoder) have been available in whatever size, as long as you had the money to spend. Now steppers are available in some pretty large sizes. If you apply enough force to an energized stepper motor, you can get it to jump over to the next step (this is called loosing a step). A servo motor won't do this. However, this can be good and bad. You wouldn't want this to happen under normal conditions, but if something goes wrong and the machine gets hung up, it's preferable to loose steps over stripping off a gear, etc. There are more pros and cons to this argument, but bottom line: both types will work just fine.
ROUTERS AND SPINDLES
A router is a single speed (or slightly variable speed) hand held tool designed to do intermittent work with bearings designed to resist forces imparted by the operators hands.
A spindle is a three phase motor with much larger and stronger bearings, and when coupled with a variable frequency drive, is capable of reverse rotation and a speed range of between 100 to 18,000 rpm.
In a CNC environment, a router is a disposable item and is barley adequate. If you plan on actually cutting materials, just skip the router step and get a spindle. You will end up there anyway.
COMPUTERS, CONTROLLERS, DRIVERS, and DESIGN SOFTWARE
The interface and software is one of the most important parts of the whole system. However, which is best and what works for an individual's situation can be totally different from person to person. On one extreme, one can use an old PC, write the programs in a text editor, and run the CNC with a $50 shareware program operating on DOS. On the other extreme, a completely automated design, nesting, CAM, and driver set can cost as much as the machine and require a yearly maintenance fee.
Because everyone's needs are different, I can only recommend that you do as much research on the software as you would with the rest of the machine. Most of the time, manufacturer's will let you try their software on a demo basis.