How are mammals the same as vertebrates?

All mammals have a spine or a backbone. Another Word for a backbone is a "vertebra" and thus all mammals are "vertebrates".

However the presence of a backbone does not DEFINE a mammal because other animals also have backbones, eg reptiles, birds and fish - these animals are also "vertebrates".

Mammals are mammals because they are the onlyanimals to have fur/hair and feed their young on milk (there are some exceptions of non-mammals with fur and who feed milk to their young, not not many).

The reason for all these animals being "vertebrates" is because a long time ago in geological history they all evolved from an animal that had a backbone.