To me, it’s quite simple: both are essentially the same dish. Curry Mee typically refers to the type of noodles used, namely the yellow or egg noodles. Additionally, there are various styles and regional variations to explore.
I’ve also prepared a Thai-style Vegetarian Curry Laksa, which you can find in my recipe for Siamese Laksa. Moreover, I’m including a recipe for Vegetarian Curry Mee that I created quite a while back; it remains a favorite and is definitely worth a try.