Transhumanism is a philosophical movement that advocates for the transformation of the human condition by developing and making widely available sophisticated technologies to greatly enhance human intellect and physiology. (wikipedia)
transhumanism - the theory that science and technology can help human beings develop beyond what is physically and mentally possible at the present time (Cambridge dictionary).
I think its wrong to take terminology out of context. In fact I always hate it when it happens.
Transhumanism is about evolving humanity via technological means to something greater, better. Beyond human. This is positive development, and thus sees technology ultimately in a positive light as ascension.
Cyberpunk is all about technology seen in a negative light. When technology is NOT the saviour people want it to be. It controls, oppresses and enslaves people. Corporations control the technology, so Corporations are evil.
There is a fundamental phllosophical difference here. It is a "glass half full or glass half empty" kind of difference. When you install implants into you in a cyberpunk setting, it can be likened to giving away pieces of yourself so you are 'less' than you were before. In transhumanist setting it can be likened to 'improving yourself', so you are 'more' than you were before.
Some transhumanism may be present in cyberpunk stories sure, especially in those that want to resolve the story in a positive way. Transhumanism can turn the setting around and give a "good" ending to a cyberpunk story. For example in Ghost in the shell (the manga at least) the protagonist is a full-body replacement cyborg, who ponders her own existence. "The only thing that makes me feel human is the way I am treated." The story culminates with the protagonist fusing with the puppeteer (an AI) thus becoming something more than human. A transhumanist ending.
Ghost in the shell 2 explores what happens after very interestingly (although its probably very confusing for your average reader), as in the end it is revealed that both the protagonist and the antagonists are merely different digital instances of the original Major Kusanagi (who is now basically an AI).