The regular API is part of the V-REP API framework.
The regular API is composed by several hundreds of functions that can be called from a C/C++ application (plugin or main client application), or an embedded script. V-REP functions and constants can easily be recognized from their "sim"- or "_sim"-prefix (e.g. simHandleCollision). Make sure not to mix-up the regular API (sometimes also "API" in short) with the remote API.
The regular API can be extended by custom lua functions, that plugins or the main client application register. Custom lua functions can be recognized from their "simExt"-prefix.
All units going to, or coming from the API are in meters, kilograms, seconds and radians (unless otherwise explicitly indicated), independently of what was selected for the user interface units in the user settings dialog.