Does changing your pronouns automatically mean someone is transgender?

I don’t mean to be rude or ignorant on the topic, even though I’m a youth and probably should understand all this well, I’m still learning. To me, there’s a ton of things changing in this world that I can’t seem to keep up with.
My grandma recently referred to the cashier at the grocery as “she”, the person politely said he uses “he/ him” pronouns, i understood and apologized on her behalf. He was cool about it, and he actually knew my grandma for over a decade so he was willing to teach her as well. My grandma was confused lol but I guess she sort of grasped the pronouns topic. But then came the topic of transgender and pronouns and this is where I myself got confused and the cashier proceeded to bash me, and call me ignorant. I had just asked a question out of good intentions. I had honestly thought that if someone changed their pronouns, that doesn’t necessarily mean they’re transgender. I thought being transgender was doing some sort of medical procedure to remove the sex parts and/or take hormone meds. But the cashier started arguing, while I was standing there quiet lol.

If anyone would explain to me this whole topic I’d really appreciate it. Thanks!
Does changing your pronouns automatically mean someone is transgender?
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