Gohan vs Shoku

I have heard these words used interchangeably and my coworker is having a hard time explaining in English. She told me there is no difference just difference in politeness.

gochoshoku--->asagohan
gochushoku-->ohirugohan
goushoku-->ouhan

Can you explain a little more?

Yeah, I kind of think of it like the words "dinner" and "supper" in English. they both mean the same thing, but I feel like "dinner" is a little more informal out of the two.

You have encountered one of the hardest things about learning Japanese for native English speakers. That is, when something exists in Japanese, but doesn't necessarily exist in English as well.

The best advice I can give is to let go of having to have Japanese line up perfectly with English. There are going to be a lot of times where a word or phrase only makes sense in Japanese. Best to just accept that fact and more forward with it.

shoku 食事　食　derives from "a meal" 
gohan ご飯 derives from "rice" 

Could be more of a historic thing when all meals consisted of rice and as languages and cultures evolve the words change to be more inclusive of food where as these days Japanese food consists of more than just rice.