Player Boost and MSQ

[Kirika-]

Character Level boost effects your character's progression in the MSQ, as in you will effectively have passed all the direct MSQ steps to get to level X.
Character Job boost effects the job you buy the boost for, to boost it to level X, however if you haven't progressed your character to at least that level or higher, you can't job boost.
MSQ boost effectively skips the MSQ content for your character, assuming your character is high enough level.

So, yes, boosting effects your character as a whole in regards to the MSQ, even if you decide to try other jobs.

Remember, unlike most all other MMO games, your character is capable of obtaining every job in the game and leveling them to max level, so your character is your job(s) in FF14. Were as other games, your job is your character, as far as leveling and progressing and that you can't easily change.
FF14 - Be all that You can Be!

[DPZ2]

Character Level boost effects your character's progression in the MSQ, as in you will effectively have passed all the direct MSQ steps to get to level X.
Character Job boost effects the job you buy the boost for, to boost it to level X, however if you haven't progressed your character to at least that level or higher, you can't job boost.
MSQ boost effectively skips the MSQ content for your character, assuming your character is high enough level.

So, yes, boosting effects your character as a whole in regards to the MSQ, even if you decide to try other jobs.

To be clear, the individual 'job' boost is available for a level 1 character, and will complete all of the job quests, through level 70 at this point. It does nothing for the MSQ, nor do you have to qualify to use it by first getting a level 70 character up-and-running.

The 'story-line' boost, on the other hand, is also available for a level 1 character. You may purchase the "end story" through A Realm Reborn, or through Heavensward, or through Stormbringers. Once used, your level 1 character is still level 1 and cannot run further storyline quests until your character achieves max level for that boost, unless you also purchased a 'job' boost.

You can always 'job' boost at any point in the game. It doesn't make a lot of sense unless you want to run that level 60 Gunbreaker through the main storyline, where they receive little except the XP assigned to the main story quests and side-quests, since all of the monsters out there are too low to provide XP.

You also can't do any content beyond current MSQ quests -- since instances are triggered by reaching a point in the MSQ. Gunbreaker has to suffer through all of the MSQ up to the first dungeon to be able to queue for that dungeon. Rinse. Repeat.