The simple definition of 'transgender' is that you don't identify as the sex/gender you were assigned at birth. It's technically an umbrella term, even though it usually refers to those who identify as the opposite binary gender. I know someone who is genderfluid and strongly identifies as trans. Others consider themselves gender nonconforming, more than trans. That's where I am. Gender variant is another term I've heard.

What it comes down to is that only you get to decide how you identify. You can be genderqueer, nonbinary, bigender, pangender, genderfluid, agender, or whatever feels right to you. You don't need to want to transition.

Gender dysphoria means you're experiencing emotional or psychological distress and that's a mental illness. It's the distress that's the problem though, not your gender identity. Depression and anxiety might be separate issues, or they might be connected to repressing your true self. It might very well be that if you were able to accept and express yourself as a trans or gender nonconforming person, the distress, anxiety, and depression might improve. It's something that you might benefit from talking to a therapist about.