There are two basic approaches depending on whether it is better to physcially copy the data from one table to another (Tables, not layouts) or to just add fields from the "look up" table to the other table's layout.
See this link for a discussion of both methods: Auto Fill
Is it possible to have this occur if I am using layouts for both and not tables?
Layouts and tables are two very different things even though the name of a table and a layout is often the same.
Every layout refers to a table. Unless both layouts refer to the same table in Show Records From in layout setup, moving data from one layout to another actually requires moving the data from a record in one table to a record in the other. That's one of the two options discussed in that link. The other option avoids moving any data, but instead just uses the fields from the related table to display the data.