Climb up and Come up

Climb up verb - Go upward with gradual or continuous progress.

Come up and climb up are semantically related in climb topic. In some cases you can use "Come up" instead a verb "Climb up", when it comes to topics like go up.

Come up verb - To come near or nearer.

Climb up and come up are semantically related in climb topic. Sometimes you can use "Climb up" instead a verb "Come up", if it concerns topics such as go up.