This sounds like the same setup in the FileMaker 11, contact management starter solution.
If so you have multiple occurrences of the same table. Many parts of FileMaker refer to a "table" when they are really referring to a table occurrence--one of the boxes in the manage | database | relationships windows.
You can create multiple occurrences of any given table in order to link a table to itself in a relationship and in order to define more than one relationship between the same two tables.
To learn more about table occurrences, see this tutorial: Tutorial: What are Table Occurrences?
You've identified the situation, a "self-join". That's additionally confirmed by the entry for that file in the "Tables" tab. Under "Occurrences in Graph" it mentions Contacts, Similar Company, Similar Name, and Similars.
With the second button under "Tables / Relationships" (the one with the pointer, the table, and the plus sign) I can create another table occurrence. This adds a second item to "Occurrences in Graph", which is what I want. It confused me at first that the new table occurrence showed all the fields of the original table, but then I discovered that the control in the upper-right corner toggles between showing (1) just the table name, (2) the table name and the match fields, and (3) the table name and all the fields.