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I've had a few people ask me this question recently, so I thought I've leave a little info. Feel free to add additional info down below and include some universally unlocked device you've had experience with.
The difference is quite simple.
Unlocked phones can work on multiple GSM carries such as T-Mobile, AT&T and their MVNO's (given the correct bands).
Universally Unlocked phones will work on all 4 major carriers (T-Mobile, AT&T, Sprint & Verizon) including their MVNO's (again given the correct bands).