First, an important detail. Layouts and tables are not the same thing. You are describing moving data from one table to another via a change in layouts. You can have many different layouts that all refer to the same table.
The best option may be not to copy the data at all. A relationship that links the records in the two tables can enable data in one table to be displayed on a layout based on a different table. In other cases, a script can use set variable to set the value from a field in one record and then the script can change layouts (to establish a "context" that refers to the other table) and then it uses set field to set the field with the value from the variable.
You don't want to use the actual copy and paste script steps for this as copying data in your script will destroy any data the user may have copied to the clipboard and having copied data disappear when they run your script tends to confuse and irritate your users.
You'll need to describe what you have and what you want to do in more detail before I can suggest the best option for you.