It is not clear to me what you mean by "table format".
You can certainly enter Manage | Database | Tables, select a table and then click "Copy". If can then click paste in this file or any other Filemaker file to paste a copy of the table into your database. This copies the design of the table, but not the data. However, this can only be done with FileMaker Advanced.
In FileMaker Pro, you can also duplicate a table if you use Import Records with the "new table" option selected for the target table. This does also import data, but since Import Records imports data from the current found set, this need only be a single record that you import and then delete.
On the other hand, you can go to Manage | Database | Relationships, select a "box" on the relationships graph and click the duplicate button (two green plus signs) to get a duplicate Table Occurrence. This does not duplciate any table, but does produce a new way to reference the existing table for use in relationships.
In none of these cases is a "new relationship created", so I am puzzled by what you mean by that.
And none of this has changed in recent releases of the product.
If what you really mean is that you want to copy a layout. Duplicate Layout will do that for the existing file and you can enter layout mode, select all layout objects and then copy them to the clip board. You can then navigate to a different file and layout in order to paste them. This can be made to work, but a great deal of attention to detail must be paid. You may even find it useful to paste the layout, import the scripts performed from buttons and script triggers on the layout, then paste the layout again. You also have to pay attention to the tables and table occurrences in the target file.
This also is a process that has not changed for many different versions of FileMaker.