Firered and leafgreen both can catch different Pokemon but there pokedex is the same, here is some examples: magmar only in leafgreen not firered, oddish in firered not leafgreen, ekans in firered not leafgreen, bellsprout in leafgreen not firered, pinsir in leafgreen not firered.
you cant trade Pokemon from pearl to firered. you can only trade from firered to pearl because firered doesnt have the data. in other words no sinnoh Pokemon are in the firered pokedex and is completely unknown. No but you can trade fire red Pokemon to pearl