'Staycation' is a new word as it is, the 'domestic holiday' way I and many others use it is barely any newer that the way that the 'day trips from home' people use it. I think that makes a difference, it is merely a different usage, with neither being correct nor incorrect.
But why would you even think to need a different word, unless you're actively trying to belittle UK holidays - of the sort that a great many people can only ever afford to go on (or do for other personal circumstances), and enjoy very much?
"We're off on our holiday next week."
"Ooh, lovely - where are you going?"
"California/Pembrokeshire/Ibiza/Bangkok/the Lake District"
"Sounds great - hope you have a wonderful time!"
To me, if somebody going on an actual UK holiday felt the inclination to refer to it as their 'staycation', that would indicate to me that they're at pains to point out that it's not their 'real, proper holiday' - lest anybody should think badly of them.
It reminds me of the people who will always unnecessarily say "I need to charge my iPhone" or "I'm nipping out to get some super unleaded petrol for my BMW" - unless you're Alan Partridge, it's just tedious extra detail designed to try to put yourself in a better light.