Many producers convert their tracks to audio to begin mixing... it's not a hard and fast rule, but it's typical.
Logic will not save your instrument tracks as audio unless you specify this is what you want.
If you have NOT drawn volume and pan automation on tracks, then you can select:
File > Export > Export all tracks as audio
(This will export all tracks in the Arrange area to audio tracks)
If you want to export them to audio individually solo a track, set the locators:
File > Bounce...
(click on add to audio bin if you need to quickly add the audio tracks back into your project).
Once you have audio regions on audio tracks in Logic you can make some changes to the sound... but it's not as flexible as manipulating MIDI regions or software instruments.
for example, changing a note's pitch on a MIDI region is a simple task in the Piano Roll. Not as simple on audio regions!
The moral of the story ;) is to find out whether the other Mac has the same plug-ins and instruments you are using. If you are using plug-ins bundled with Logic Studio, then any other Logic Studio user will have access to the same instruments and plug-ins.
The only issue will occur if you are using 3rd party plug-ins on some tracks (in which case bounce those tracks to audio) and your own samples and audio files (in which case save these to your project folder).