Layouts and tables are two different things in a FileMaker file. Every layout is linked to a specific table by naming a "table occurrence" in "show records from" in Layout setup.
Here's how to create a "Clients table":
Open Manage | Database | Tables
Enter "Clients" in the table name box and click create. You have just created a new table.
Filemaker, to save you time, has also created a "table occurrence" of the same exact name. Click the Relationships tab. On it, you will find a "box" that is also named "Clients". This is an "occurrence" of your new table. Hover the mouse over the upper left corner and the name of the occurrence's data source table will pop up. Since both have the same name, you see "clients" as the table (data source table) and table occurrence names--which can be confusing to newcomers. At this point, just keep in mind that you can create additional occurrences of the Clients table on the relationships tab and give each a different name. We do this in order to create different relationships between the same two tables.
Now click OK and check your list of layouts in the drop down in the status area. You'll find you have a new layout named "Clients" has been added. Select this layout and enter layout mode. Select Layout setup.. from the layouts menu or by clicking the pencil icon next to the layouts drop down. Note that you have a drop down list here named "show Records From" and that "Clients"--the name of the table occurrence for your clients table has been selected for you. Note also that there's a text box here where you can change the name from "Clients" to any other name you might find useful. Changing the name does not change the choice made in "Show Records From" and thus changing a layout's name doesn't change the table it refers to.
Just to make the differences more obvious, return to Manage | Database | Relationships. Double Click the Clients table occurrence and rename it as "ClientsTO". If you hover the mouse over the top left corner or check the tables tab, you'll see that this name change did not change the name of your data source table, Clients. Now return to the layout and check layout setup on your Clients layout. While this did not rename your layout, Show records From now lists "ClientsTO" as the table occurrence specified for this layout.
To learn more about how table occurrences control a FileMaker database, See this thread: Tutorial: What are Table Occurrences?