The definition of entrometido in the rae just sends you to entremetido.
Is there a real difference between the two? And if there isn't then why are there two words with exactly the same meaning. Maybe something to do with its origin?
The Diccionario Panhispánico de Dudas has this to say regarding
To put it more clearly: the meaning is the same but when you are using it as synonym for
So they are synonyms and it means a person who intrudes into other people's affairs (meddler or meddling person). At least in Spain entrometido is the one used for this meaning. I have never heard "entremetido" (though people would guess the meaning).
As you can see with Ngram Viewer now entrometido is more common though entremetido was common in the past.
Also entremetido can be used as a participle of the verb entremeter. In that case it can mean to place something between other things. But I'd say that "meter entre" is more common than "entremeter" (at least in Spain).