Yes completely! I play my P bass very differently to my Smith. I deliberately keep them both because they sound, feel and play totally differently. Together they cover a lot of ground.
The synth equipped basses are different again; obviously my mini bass is completely different and my Vigier feels like an old favourite jumper.
The proof for me is that if I pick up a bass I don’t like (aesthetically or in feel) then I just don’t feel inspired to play anything in particular.
Guess it’s like cars - I drive my big estate car quite differently to my previous saloon shaped one even though they have the same engine. You just pick up in the vibe from the object, be it bass, car, whatever. If there’s no vibe then I move on to something else.