I couldn't reply earlier as I was busy with my academics. ( I was still in college you know)
The distinction is that an 'Asian in' has a floating strike and 'Asian out' has a fixed strike.
For simplicity let's consider how a call option works for both in and out.
S=Settlement price
K=Strike
We know that the payoff at maturity is (S-K,0) for calls.
The former i.e Asian in has a fixed strike(decided at the beginning of the contract) and a floating settlement price(taken as an average of Asian setting date prices).
The latter i.e Asian out has a floating strike(taken as an average of the Asian setting date prices) and fixed settlement price(i.e the price at maturity)
This is analogous to the lookback option types