Explanation by Laura Baker. The difference is in the part of speech.
This is an everyday occurrence.
–Everyday is an adjective used to modify occurrence. The sentence means that this happens each day.
We are just your average, everyday people.
–Everyday is an adjective to modify people. The sentence means that we are average, normal people.
This happens every day.
–Every is an adverb to modify day. It is not just some days that it happens, but every day.
I go to work every weekday.
–Every modifies weekday. This means that I don’t go to work on the weekends, just every weekday.