So I just recently realized the difference between the two through combinatorics . So for example with a range of 88+,AQs+,AQo+ vs QQ on a 553 board our equity is 68.94% but we are ahead 79.51% of the time. When and why do we base our plays on which or is one just flat out better, I'm confused now.

Say we play a coin flipping game with a fair coin.

Every heads you win $1
Every tails I win $5

How many times do you play this game?

You are ahead 50%
Your equity is about 17%

What's the point of estimating equity? besides a situation that goes AI? I just can't see situations where estimating how much I'm ahead outweighs estimating equity or to use both. I'm confused of their applications.

In the case there is no money put in the pot, we can estimate if a play is profitable or not and/or how much money we can make in the case we bink one of our outs on future streets and win more money.

It's all about how much money we are expected to win, that is, our EV. We use equity to describe our EV.

Estimating your equity is crucial when you get involved in big pots, because it is your equity that you should be comparing with the pot size and the price of calling.
e.g. If you bet the flop with TPTK, and villain raises when there are no obvious straight or flush draws, you should quickly realise that you have very little equity. Against a set, you're practically drawing dead (you'd usually need a runner-runner flush/straight suckout). If villain makes a minraise, you might have pot odds of 3:1 or 4:1, meaning you need 25% or 20% equity to make a breakeven call, but you almost never have this much equity unless you're on a straight/flush draw yourself.
If, on the other hand, you estimate your equity to be close to 50% (and especially if it's greater than 50%) you should be willing to stack off immediately. When you have a combo draw that gives you at least 45% chance of winning at showdown, shoving the flop is a good option, because you probably also have some fold equity too. There's also some dead money in the pot, so you make money in the long run whether villain folds or calls.

Here's a quick example where you're ahead on the flop, but (counter-intuitively) are not expected to be be best at showdown.

Board: Q25
*******Equity*****Win*****Tie
MP2****45.62%**45.62%***0.00%*{ QsJs }
BU*****54.38%**54.38%***0.00%*{ AhKh }

You have TP with QJ, but villain with AKs is the favourite to win, at least at this point. If villain showed you his cards, you'd obviously bet as you have the best hand. If he shoves, you'd call. Although you'll only win the hand 45% of the time, the dead money would make it just about break even.
If villain merely flatted with his monster draw (NFD+ 2 overs), then you'd see a turn card. If it was a blank, QJ would suddenly become a big favourite, with about 65% equity. You'd obviously bet again. If we ignore implied odds, villain would be making a mistake if he called more than half pot. Thus we see it's better for the drawing hand to get the money in on the flop when he's a favourite, instead of waiting till the turn when he'll be a big dog.

Who cares how often we are ahead at some arbitrary point? I care how much money I'm expected to win (or lose) when the hand is over.

Note: "Ahead" is even a vague term. I would actually describe the hand that is expected to win the most when the hand is over as the one that is ahead, as opposed to describing the hand that would win at the current point if we stopped playing at said point as being ahead. As an example on a 7h6h2s flop, I would say that 9h8h is ahead of AsAc, though if we decided to not deal the turn and the river, AsAc would of course win. Assuming we do deal the turn and the river and 9h8h is up against AsAc, 9h8h will win more. Of course we do deal turns and rivers. Therefore, I will take the 9h8h in that situation.

The amount of times iv'e been called a fish or words to that effect for getting a draw in as a favorite.

Its not just equity your weighing up though you need to assign villain a range of hands that he can have and then see how your hand stacks up equity wise vs that range, this can drastically change the way you will play a hand or a street. Also theirs fold equity which when weighing up a hand can decide if shoving in a certain spot with your fold equity+hand equity can be profitable. Also facing tricky river spots with say ace high you can weigh up how often villain bluffs then determine how much equity you'd need vs that bluffing range to make calling profitable.

We always use equity.
On the river estimating equity is the same as estimating how often we are ahead.
This might have caused the confusion.

Sometimes we take a shortcut to equity.
When we have JJ on a low (7-high) board vs a villain who can only have an overpair (he would've played 2p, sets and 2overs different);
We don't have to calculate equity; we just count 3 pp's below us, 1 above us (when we know AA and KK are not in his range). We are ahead 75% of the time.
(actually on the flop 70-30; turn 72-28; riv 74-26).
We know we can use a shortcut because (as homework) we did both and saw they were close enough to use both (and counting times ahead is simpler than estimating equity).
That said, this only works in situations where the equity-chunks are equal.