ChrisSlicks

The throttle position sensor, also called accelerator pedal position sensor (yes it's the same thing) measures purely the position of the pedal. Like you stated it sends a varying voltage to the ECU, likely between 0 and 5V but the scale is irrelevant. There are 2 sensors for redundancy and safely but they are named the same thing, even though the redundant sensor may be on a different voltage scale (e.g. 0 - 2.5V).

The ECU samples the position sensor voltage somewhere between 50 and 100 times a second (depending on exact vehicle). From this it not only determines the position but can also determine aggressive movement by abrupt changes in voltage. How the car reacts to these inputs depends on the original programming of the ECU and the loaded tune. The signal is also forwarded to the TCM (Transmission Control Module) so it can decide whether your throttle input warrants a new gear selection, and holding gears.

As already stated, a tune is the best way to "remap" how your throttle input behaves.