Plenty of parents pour a cup of water over their baby's head at bath time and figure they're doing a version of what a swim coach would do. It's a reasonable instinct, and it does help a little, but the two environments aren't as similar as they seem.
Comfort with water on the face and general lack of startle response definitely transfer from bath to pool. A baby who's used to a warm washcloth over their eyes tends to handle a coach's first splash better than one who's never had water near their face at all.
Buoyancy, temperature, depth, and the sheer scale of a pool are all different enough that a baby's bath confidence doesn't automatically show up in the water. We've had plenty of "great in the tub" babies cry through their first pool minute, which is completely normal and usually passes within a lesson or two.
Bath-time comfort is a good start. Lessons build the rest.
See Baby Program