Greek letters / spelling out letters

[RCM2020]

I was recently at a fraternity and sorority life conference (I'm an undergrad) and I noticed many of the other students with me wore philanthropy or formal or date party shirts that had the letters of another organization. For example, I saw a SigEp wearing a shirt that says "ΔΖ turtle bowl." At my school, if delta Zeta sold a shirt, they would have it spelled out "delta zeta."

I asked one of the students about this out of curiosity, if people can wear other letters. He said yeah, and an advisor walked by and joined this conversation. I explained that my school spells it out, and the advisor asked me, what's the difference? And to be honest, I didn't have an answer. She even told me there isn't even a national policy about wearing other letters! (Maybe organization based though)

Is there a difference by using your Greek letters or spelling it out? Do they both not mean the same thing? It seems silly but I've never thought about it that way. This year we changed our philanthropy shirt design by removing our Greek letters on it and spelling it out so we could sell to other students. But did we really have to? Are these just unspoken rules?

I'm curious on other opinions.