Is cologne a perfume?

Cologne and perfume are both fragrances. But cologne is not perfume.

The difference is the dilution.

The strongest is "perfume extract." It is what they make all the other kinds of fragrance out of. It's approximately 20 percent aromatic compounds like essential oils, the rest is alcohol. This comes in a 55-gallon drum so you probably don't want any.

Cut it 1 part perfume extract to 1 part alcohol (or "1:1"), you get eau de parfum.

Cutting eau de parfum 1:1 with alcohol gets you women's eau de toilette or men's cologne.

Cutting that 1:1 with alcohol gets you women's eau de cologne.

And cutting that 1:1 with alcohol gets you women's splash or men's aftershave.