If you save and quit out of the game and load it back again the game puts you always at the last valid savepoint. Sometimes that is one you manually saved at, sometimes one saved by the game as you traversed a portal, or an autosave point during the tutorial. This allows for a very useful position manipulation on the map. In the proof below you can see the use of this technique in the tutorial section of the game.
If you fast travel you do not save at your destination savepoint .
If you enter or exit the breach through a portal, you typically save in the corresponding room (if there's a savepoint).
Breach storage means you have separate savepoints for the breach and overworld.
You can claim a savepoint with the drone and recall it to savequit with Indra and let her spawn there. Used in the early Giguna strat for example. This is called character warp from now on.
Entering the Emergence via the freight elevator sets your savepoint to the Emergence.
Exiting the Emergence via the freight elevator sets your savepoint to the one immediately west of the facility (23, 22).