I learned from the dictionary that a crate is a wicker basket, then what is a dog crate? Isn't it the same as a dog house?

HAHA well, they are more or less interchangeable. To contradict what I just said, a dog kennel can be a place to take your dog to be looked after for a while. A crate is nothing more than a sturdy box to put a dog in. Could be metal, plastic, or any other material.

Dog "crate" can be anything portable.
Dog "kennel" is not portable and is usually found outdoors or it could be somewhere you can board (leave your dog for someone to care for) while you are on vacation.

Dog "crate" can be anything portable.
Dog "kennel" is not portable and is usually found outdoors or it could be somewhere you can board (leave your dog for someone to care for) while you are on vacation.

In the UK (or at least my part of it), a kennel is made of wood or plastic and is usually an outside shelter. I think the US terminology is 'doghouse'. It can also be a structure of individual outdoor runs and shelters for many dogs. A crate would generally be perceived as a travel-cage for transporting a dog when outside the house; crate-training whereby a metal or plastic cage or crate is used for indoor housetraining is fairly novel here.

Essentially, the words are interchangeable.

A dog crate is wire, plastic, wood etc.. Plastic crates are better. The term Kennel can also mean crate.. But it's generally a fenced run outside. Different areas, use different terms regularly.