Each machine makes a basic running stitch the same way, with two sources of thread. The top needle takes the thread down into the fabric. It is caught and looped via the bobbin apparatus and then pulled back up. The "feed dog" (a rough edged surface underneath the fabric) moves it along and the next stitch begins. Everything else is different.
Mechanical Sewing Machines
A mechanical sewing machine is controlled by a rotary wheel. Any adjustment like the tension or the length or width of the stitch is made by moving a dial. These machines are very basic and tend to be less expensive than the other sewing machines.
Electronic Sewing Machines
An electronic machine differs in that there are some functions that can be accomplished by pushing a button. A machine can have a number of motors for various duties and they are run via electricity.
Computerized Sewing Machines
As sewing machines became more complex, more of these motors were added. A computer then coordinates all these functions. Think about a repetitive sequence of stitches being programmed, so you no longer have to replicate these movements over and over again. Nice!