Theoretical analysis is saying: White has an advantage with best play for both parts.
Objectivly (I don't like this word, I prefer Practical) it's easier to play as black.
Lets take the Smith-Morra Gambit. Theoretically, black has a slight edge (or equal game), but practically it's perfectly playable for white. If black makes one mistake, hes toast. If he doesn't, he'll have a pawn. But avoiding making a mistake for around 20-25 moves, while defending and analysing sacs on d5 and e6 is VERY difficult. If black misses a finer point about the Bd5, he'll get mated. If white miss it, he can probably find another sac in 2-4 moves.
That is what I understand of Theoretical vs Objectively.
I have sometimes come across chess annotations in which comments have suggested a difference between the theoretical and objective assessment of a certain position. For example, I've heard IM Andrew Martin make a comment "this position may be theoretically better for white, but is objectively more playable for black" (or something like that).
I am really confused. I thought that a theoretical assessment would be the same as an objective assessment. I hope someone can shed some light on the use of these terms.