Basically an AWD may not be a full-time system, i.e. it only drives the front or back wheels until it detects slippage, in which case it transfers power to all four wheels. Or it's full time 4 wheel drive, but low range gearing selection is available.
A 4x4 on the other hand usually has a low range shift, for really difficult conditions.
Personally I would rather have 2WD with snow tires than an AWD with all-seasons. This year I went with the Nokian RSi's, however next year I think some Hakka4s with studs, the RSi's had a little bit of slippage over ice.