I think this isn't always true because they do mean different things. You're not an "immigrant" unless you're trying to stay there permanently, whereas "expats" can be sort of transient
I do the reverse thing of calling myself an immigrant and you can see people having an error in their heads. Because I am an immigrant, I came here unemployed with nowhere to stay, looking for a better life. But I'm white, so expat it is for them 🤷