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It's the same thing. As for if you will see frame tearing under the adaptive sync range, then that's going to depend on how sensitive you are to it.
They are the same thing. Freesync was just a slang term when the technology first came out to refer to AMD's Adaptive Sync. The term "freesync" eventually caught on to the point where everyone including AMD themselves started referring to the technology as "AMD Freesync".