Hey LeOsTyLe,
To put it simply, how much damage your Pokemon RECEIVES depends on your POKEMON TYPE and the type of attack it's suffering.
How much damage your Pokemon INFLICTS depends on the ATTACK TYPE against the Pokemon Type of your opponent.
Example, imagine you have a Blastoise (Water Type Pokemon) and you're attacking a Charizard (Fire Type Pokemon). Water attacks like Water Gun and Hydro Pump get the x1.25 damage boost. However, if your Blastoise has an Ice Beam secondary move, it would actually suffer a x.8 loss in damage because Fire Pokemon are resistant to Ice attacks. Just because Blastoise is a Water Type Pokemon doesn't mean his Ice Beam will be stronger.