H(10$):As2s
V(20$):We know he has QJ

Pot:10$
Flop: 10h 8s 9s
V: Bet 10$
H: Call All-in 10$

In this situation, we need to hit our flash to win and we have 35% of doing that by the river. That translates to 2-1 pot odds so calling here should be fine.

Now let's imagine we both have bigger stacks and repeat the flop:

H(100$):As2s
V(100$):We know he has QJ

Pot:10$
Flop: 10h 8s 9s
V: Bet 2$
H: Call 2$ (we have the right odds to do that)

Turn: 3c (pot: 14$)

V:Bet 8$
H:?

Now here it's getting interesting. We need 2.75 pot odds to call that bet but now our chance to see the flash by the river is 20% which translates to 4-1 pot odds. We definitely don't have the right odds and should be losing money over long term.
BUT if you look from another perspective, calling here would put us on the exact same situation as the first example with the all-in. That means that we paid a total of 10$ into a pot of 10$ (to see turn and river), so over long term calling here should have the exact same result as in the other example, which means we shouldn't be losing money right?

No. The situation changed.

In situation one, you have the chance to call and roughly break even, because you're paying $10 to see two cards. Your EV on the flop is just above zero.

In situation two, you should ignore the fact that you've already paid $2. That money has gone. You're now faced with paying $8 for one card. It's not profitable to do that.

I know about the 'the money has gone focus on your current bet' rule but I was trying to understand what the difference is, because in both situations I paid 10$ in a pot of 10$ to see 2 cards.

But I think I figured it out. In example 2 I am only considering the games where my spade doesn't hit the turn and villain bets. But if the spade DOES come on the turn, I can't guarantee that villain will put another 8$ to break even with the situations where it doesn't hit the turn so here's where my math goes wrong.

If u could take back $8 on a brick turn in scenario one, would you?

The difference is information.

In spot 1 you only have the statistical likelihood of how the next 2 cards are going to fall. If M is a card that misses your draw and H is the card that hits then the potential outcomes of your call are:

MM
MH
HM
HH

When you call $2 and then miss your potential 2 card outcomes are reduced becuase you have seen one card:

MM
MH

Since these are the only 2 outcomes that begin with miss.

Thank you all for the replies.

@YouAreAwesome Indeed I'd take my $8 back. When we made the $10 dollar bet, we got (almost) equal chances of hitting our card flop>turn as turn>river so we can say we paid 5$ for each street. After paying $2 for one street it's absolutely worth it to take 8$ back on the turn and be happy with the cheap turn peek. If I was offered $5 instead, I would choose to see the river instead (a $5 bet on the turn would give us the pot odds anyway, $5 to win $25 is 5-1 odds, which is good enough.)

@just_grindin You're right.