You can use them interchangeably 99% of the time!

The feeling is a little different, though. "I'm going" is a little more casual than the longer "I'm going to go."

Plus, only "I'm going" can be used when you're literally on your way. If someone calls you while you're walking to the store and asks what you're doing, you can only say "I'm going to the grocery store." You can't say "I'm going to go to the grocery store."

They are both fine, they mean the same thing, you are making a statement telling someone else where and what you are going to do

Thank you Christa and Mercy! It's clear now.