Quote Originally Posted by housefish17
Alright let me see if I get this straight.

Lets just say with any given hand, against a range of villain hands, I am a 55% favorite to win after the flop

If there is 40$ in the pot, I am due 22$ of that if we both pushed all in?

You are due $22 if it is checked down. Obviously if you go allin then you will be due a percentage of that bet aswell so you will be due more from the total pot, but it might be that you are now due less than the total amount you have put in which is bad.

Does equity only apply when you go all in?

Im not sure I understand this question. Equity always applies

Also, does that mean equity is essentially the same principle as pot/implied odds?

It relates to pot odds yes. Not really implied odds though.

if you have 18% chance of hitting your nut flush with one cards to come, that means that any bet less than 18% of the pot on the flop is going to be +EV?

yup

Lets just say the pot is 100BB and you have to call 20BB to see the river for ease of math and if you don't hit your hand on the river, you check/fold

Yea thats just about break even with a flush draw. Then you consider your implied odds and its an easy call.
Even though equity really has units of money, you will most commonly hear it talked about as a percentage since percentages are easy to remember for common situations while dollar amounts are different in most situations.

You will commonly see people saying things like

He makes a $50 bet. If I push in over the top for $150 I expect him to fold 35% of the time and call the other 65% , but when he calls I have 30% equity. And then from this they work out if a push is good or not.