I have a table with contact information for potential business contacts. The ‘type’ field in the Contact table is single select field with three possible options. If ‘type’ = ‘client’ in the Contact table I would like to copy every attribute for that entry into a new Client table.
If I understand you right, both tables are pretty similar. The tables should be linked together. In Excel you can derive data from other sheets just by formula, but not in Airtable. Tables have to be linked.
May I suggest an idea: Airtable has a powerful feature called Views. Personally I would store all data in one single table, and create a view for Clients and and a view for Potential Contacts. By using a Single (or Multi) select type of field you determine in which view the contact will appear.
This will save you a lot of headaches.