Yeah, all these words mean different things to the Social Justice/Progressive left and the rest of us.
It's one of the surest tells that a movement is wrong when they refuse to use the regular meanings of words and start redefining them in their own usage. People who are right never have to resort to such contrivances.
You're absolutely correct, and this illuminates an aspect of the controversy that I don't think gets quite enough coverage: where did the social justice/progressive left students learn about the terminology and ideology they advocate?
They almost certainly didn't learn it in high school, from their peers in high school, or from their parents. (Although that may be changing.)
They learned these things at the university, from professors, and from fellow students who learned from the same professors.
In other words, academia brought this situation upon itself by teaching these things to students -- -- so I'm rather leery of analyses which blame millennials for pushing a self-indulgent worldview on universities. If the same ideas had been taught to previous generations of students, they too would have advocated trigger warnings and safe spaces.
Which is why I'm sure you use the word "colored" (or worse) instead of african/african-american, homosexual instead of gay, tranny instead of transwoman/transman, and similar?
After all, words are just irrelevant symbol strings on top of a meaning, right? If you're not really racist, it shouldn't matter if you only ever refer to people of the global majority by slurs. The surest tell a movement is wrong is when they refuse to use the regular meanings of words.
If we're trying to communicate and understand the world together, what specific words we use don't matter, only that we agree on what they mean. We could even speak a completely non English language.
If you're instead trying to show which American political tribe you belong to, the concerns you mention become very important.
It's one of the surest tells that a movement is wrong when they refuse to use the regular meanings of words and start redefining them in their own usage. People who are right never have to resort to such contrivances.