What is the difference between "closed traffic" vs "stay in the pattern" request? My instructor made "request right closed traffic..." call before practicing a series of landings. Just wondering, what is the difference between this request and a "stay in the pattern..." request? Which one should I use when?
Actually, "stay in the pattern" is non-standard phraseology and shouldn't be used, even though it means the same thing as "closed traffic".

Specifying the direction isn't required but it is a good idea to ensure that everybody is thinking the same thing.