No, the protocols are different. DP Adaptive Sync basically has the monitor's display controller tell the GPU what range of refresh rates it can handle (e.g. 30Hz to 60Hz), and the GPU will conform to that, buffering/discarding/duplicating frames when necessary to keep things in the range the controller can handle. G-Sync uses a much higher spec custom display controller (currently a very high end Altera FPGA, but potentially could be implemented as a much cheaper custom ASIC) and will do all of its processing on-board, with the GPU just sending out frames as it renders them.
Which approach produces the superior output remains to be seen. We'll have to wait for DP adaptive Sync monitors to actually start shipping, and for them to be evaluated in a like-for-like scenario (no mucking about like 'comparing' a 2560x1440 144Hz G-sync TN monitor to a 1920x1080 60Hz DP Adaptive Sync monitor).