Hi there,
Sam from Moz's Help team here!
The reason this is happening is because the Mozbar is now pulling data from our brand new link index, whereas OSE is powered by the old link index.
The way we index the web for Link Explorer (which is now powering the Mozbar) is a bit different than the way we index for Open Site Explorer. With OSE, the index updates only about once a month whereas new data is added to Link Explorer every day. The index for Link Explorer is a different index than the Mozscape index used for OSE and includes a lot more data- we’re seeing more of the web with the new index which is helping to provide more accurate data on which to base these metrics.
In addition, the algorithm we use to calculate DA has been updated with this new index to better correlate with Google’s actual ranking standards so we can provide a more accurate representation of a site’s potential ability to rank.
Pairing the larger index of more data with an optimized DA/PA calculation will result in some changes to DA/PA. We do recommend tracking your DA and PA relative to the competitors you are tracking, as that is where the true value of the metrics is.
I hope this helps to answer your question - please feel free to send any others our way!