Does all childhood magic duplicate actual spells?

On the other hand, he’d gotten into terrible trouble for being found on the roof of the school kitchens. Dudley’s gang had been chasing him as usual when, as much to Harry’s surprise as anyone else’s, there he was sitting on the chimney. The Dursleys had received a very angry letter from Harry’s headmistress telling them Harry had been climbing school buildings. But all he’d tried to do (as he shouted at Uncle Vernon through the locked door of his cupboard) was jump behind the big trash cans outside the kitchen doors. Harry supposed that the wind must have caught him in mid- jump.

The one above is like the spell Apparition that Harry can perform. But until 6th year, Harry can’t learn it. Some other mention is Neville who can bounce when dropped, or when Lily manipulated the petal flower.

Can magic in a wizard’s childhood be re-executed when they grow up? Or at least the majority of it?