Edited to add: I had tried to quote @ElleWoods15 's response to my question but failed.
Thank you for answering.
I haven't seen anyone use "trans" and "cross-dressing" as synonyms but I would agree with you that they are not.
Cross-dressing (aka transvesticism) is sexually-driven and this doesn't apply to all people who identify as transgender. And, as you say, not all cross-dressers will call themselves trans.
As an aside, it also feeds into the myth that there is a certain way you’re supposed to dress to be a girl, and a certain way you’re supposed to dress to be a boy. And I’m guessing that actually the vast majority of both trans allies and GC posters on this forum would disagree with that.
I think you're right, the vast majority would. The difficulty comes in when "gender expression" and "social transition" come into play. Whilst trans allies and GC-type people might agree on this, I can't imagine there would be many people who identify as trans who choose to wear the clothes that are stereotypically associated with their sex. For most, wearing the clothing and hairstyle etc most commonly associated with the opposite sex will be an important part of identifying as trans.
On the theme of the thread (and as a general comment, not specifically in response to yours), I would agree with the PPs who find it odd that the Scottish government wants to mark trans day of remembrance. Whilst all murders and suicides are awful, and this day is apparently international, the murders, suicides and other deaths of people who identify as trans don't have any relevance in Scotland. Except for Tiffany Scott of course. If it's about international solidarity, I wonder if they also commemorate the International Day of Reflection on the 1994 genocide of the Tusti in Rwanda or International Chernobyl Remembrance Day, both in April according to the list of remembrance and other international days posted earlier in the thread.
It's equally odd that they continue to fund and associate with LGBTYS, given the scandals in that charity.