"cologne" and "aftershave" for "fragrance for men"

The truth is that fragrances for men, in fact what is standardly classified as eau de parfum by the concentration of aromatic oils (Wikipedia on fragrance types) are marketed as cologne. Look at www.perfume.com or www.fragrancenet.com: both categorize fragrances into women's perfume and men's cologne (for perfectly analogous products).

Why? Apparently largely for reasons suspected by OP: to avoid the word perfume. This informed article is quite explicit:

Cologne (Eau de cologne). Oldest term for perfume, used in North America for masculine scents. [...]

The paper Gendered adverts: an analysis of female and male images in contemporary perfume ads by Sandra Tuna and Elsa Freitas has this to say:

Male perfume adverts have evolved in a different way, especially because this kind of product, and its advertising, was for some time considered as mostly feminine. Thus, in the 1960s and 1970s, alternatives to the word ‘perfume’ (eau de toilette, cologne and aftershave) were preferred, so as to avoid feminine connotations, a concern that was also patent in the projection of blatant masculinity (Classen et al., 1994: 190-191). The idea that perfume adverts would make men more attractive to women continued to be exploited, and, according to the authors, contemporary adverts have become more sophisticated, but they still avoid the traditional connotations of the term ‘perfume’, and still highlight the image of masculinity, which is now combined with an idea of sensitivity.

Little wonder then if John Doe says cologne where Jane would speak of perfume.

As a side remark, my impression is that girls usually stick to the terminology provided by Wikipedia, and are particular about what product (in what concentration) they are exactly getting for their money. As remarked by Benjamin Harman, the same scent can come in a variety of products, from an extract down to a body milk, which may be viewed by some as a convenient way of adjusting the olfactory facet of their personality to a situation, or achieving a nonchallant layering effect for their scent.

No, aftershave and cologne are most definitely not the same thing. You will find at any beauty counter or perfume section of any department store that a men's fragrance, like Code by Armani or Polo by Ralph Lauren, is sold as a cologne and as an aftershave. They are two separate products, two entirely different things.

The aftershave of a fragrance is much less expensive than the cologne. It has a much higher alcohol content and has an opening in the top of the bottle that allows a man to pour it into his hands and splash it onto his face after shaving. A bottle of Armani Code aftershave costs between $10 and $15.

The cologne of a fragrance costs many times that of the aftershave, is much more highly concentrated, and comes in a bottle that usually has an atomizer at the top that allows it to be sprayed on sparingly. A bottle of Armani Code cologne costs about $100 for fewer ounces than the $10 to $15 bottle of aftershave.

If you buy a gift set of a men's fragrance, you will find that it normally contains, among other things, a bottle that is marked cologne and a different bottle that is marked aftershave. The cologne is the pricey item in that set. The cost of a fragrance's cologne's is usually six or seven times that of its aftershave. An aftershave is merely a relatively inexpensive accessory to a cologne, much like a soap or a deodorant in that same scent.

Another answer already elegantly discusses cologne versus aftershave, so I am focusing on the gender difference. As this ngram shows, there is a clear preference for cologne <=> men and perfume <=> women, however the opposite is not unheard of.

Note that the distinctions have become more pronounced recently, and were almost reversed in the 1940s. I can't explain the explosion for the (men's cologne + cologne for men) curve since 1970.