No, SampleTank 4 ("ST4") is not a DAW.
Sounds cannot be exported from ST4. What you would need is a stand-alone program that can receive the audio output from the ST4 program, and save it to disk. That's why I said it could be difficult.
But many (maybe all) DAWs allow to to load an instrument plug-in (e.g. ST4) onto a track, trigger its sounds and capture the audio output to other tracks (and save the .wav files to disk).
If you go that way have a look at GarageBand or Reaper. Other users may suggest other DAWs.