There are lots of ways that being gay and trans are similar but there are also a lot of differences. I have found that when I initially start talking about gender with someone new who has minimal queer literacy, they often get confused between sexuality and gender and conflate being trans with being gay.
Below are a lists of similarities and differences between being gay and being trans based on my experiences of being gay and non-binary and my husband's experiences of being gay and trans. We both identified as gay first, and later discovered and expressed our non-cis gender identities.
SIMILARITIES
Incorrectly assumed to be the default (cis or straight)
Living with confusion and feeling like you don't fit in before you know why
Have to figure out your identity
Have to 'come out of the closet' ie tell other people
Dealing with fear of rejection, prejudice, loss of housing or work as a result of coming out
Excitement and comfort of finding people that have the same/similar identity/experiences as you
Culture, experiences, and history specific to queer community
Lots of different terminology, language, and labels
Different interaction with people in your community than people outside of it
Risk to physical and psychological safety by living authentically
Pride parades, pride month, pride flags and symbols
Being labeled by strangers (often incorrectly) based on how you look or who you're with
Often become parents via alternative fertility methods, surrogacy, or adoption
Prejudice in health care and legal systems (significantly worse for trans identities but present for both)
Lack of appropriate/relevant sex education
DIFFERENCES
Who you like vs who you are ie sexuality vs gender
Gender based experiences and identities are much less understood and accepted by the general public than sexuality based ones (though this wasn't always the case and we hope to get to the same place with acceptance of gender identities)
Significant energy has to be put towards educating the people around you when you come out as trans that isn't necessary when coming out as gay
Coming out as gay requires the other person to change how they refer to your partner (if you have one) whereas coming out as trans requires them to change how they refer to you (which takes a lot more work on their part)
Dysphoria with trans identities that doesn't relate to gay identities
Possibility of medical intervention and changes to legal documents with transition
Difficulty accessing appropriate/competent medical care as a trans person when it wasn't a problem as a gay person
Gay community is readily available and easy to find while trans community is much smaller and harder to find
Extreme shift in privilege with transition that is much less pronounced with coming out as gay
Most trans people pick a new name, gay people don't
Let me know if you have any questions or anything you would add to these lists!