The difference between Tennis shoe and Trainer

When used as nouns, tennis shoe means a sneaker (trainer), whereas trainer means a person who trains another.

check bellow for the other definitions of Tennis shoe and Trainer

Trainer as a noun:

A person who trains another; a coach.
Trainer as a noun (sports):

A person responsible for treating injuries sustained by players during matches; a physiotherapist.
Trainer as a noun (British):

A running shoe or sneaker.
Trainer as a noun (video games, slang):

A patch for a video game that applies cheats.
Trainer as a noun (cycling):

A piece of indoor equipment allowing a bicycle to be ridden while stationary.
Trainer as a noun:

Examples:

"There was chewing gum stuck to my trainer soles."