Each layout is distinct from each other layout. You can, however, enter layout mode, select a group of layout objects (such as your fields) and then switch to another layout and then paste them. This will work very smoothly if both layouts refer to exactly the same name in Show Records From in Layout Setup... IF the layouts refer to different table occurrences (boxes in Manage | Database | Relationships ), then this may either not work at all or it may work, but be controlled by the relationship between the table occurrence named in Layout Setup.. and the table occurrence referred to in these pasted fields.
Thank you again.