Approach to learn how user matched Data Items

I have a scenario where there are rows in 2 tables and user matches one row with another, manually via UI. For example: Row1

And Row2 However, UI only allows user to select matching rows. Once user has matched rows, we don't know which column he analysed to match rows. Some column from Row1 had similar or identical value as some column of Row2. User saw this visually and matched the rows.

Now we have historical data, how can we go ahead to train system (if this is right term) to build a model such that system can match rows automatically based on historical data. Not looking for solution but a direction towards right approach/algorithm/keywords so that I can google and read better. Thanks.