Does the data really need to be moved between 2 different tables, or do you need to re-think your structure?
A bit more info on what you have and what you need, would help. Otherwise, the way to do this in Access is via queries.
Note, the examples below are just one way to proceed. There will doubtless be better ones when we get more information. Also, any time you rewrite heaps of records, do it on a copy of the database and keep a backup of the original.
1. To do what you describe -- moving one field between 2 tables.
Build a query with both tables, linking them on a common ID field (this field must be unique. If you don't have a unique field, maybe a combination of 2 fields will be unique: join the tables on both fields).
With Table A, place all fields except for the excluded one into the grid. Add the new field from Table B. Check the data, return to Design view.
Query > Make-table query. Provide a name for the new table, OK. Click the Run button (!) to create the new table.
Repeat for the reverse operation.
2. Another option -- appending the extra field from one table to another.
Same query as above, but you only create one table. The difference is that you add all fields from A, and the extra from B.
3. Third option -- you just want to replace data in table A with corresponding data in B.
Same starting query. This time, Query > Update query. Say you want Field4 of Table A to be replaced with data from Field8 of Table B. In the Update row of Field4, type [Table B].[Field8] (adjust to suit).
Run the query, and matching data will be written across to Table A.