Databses design, parallel many-to-many relationships. Two tables, or extra fields? Say I have want to create a database for expenses. 

I will have a table for holding Person details, and a table for holding Expense details. 

Then there will be two many-to-many relationships between the Person and the Expenses tables. Person Can pay an expense, and a Person can use an expense. 

What is considered better? Having one relationship table to hold both "paid for" / "used by" fields. Or two have two separate tables containing each of these fields?

Two parallel tables seems more correct, but I could also see it making the SQL more complex. Is there any compelling reason to use one design over the other?
If both fields are relevant in one record (i.e. "used by" and "paid for" can both have a person_id from the persons table), a single table is a better solution. If at least one of the two fields is always NULL, splitting the table would actually make the SQL less complex.
(Also, if an expense is either "paid for" OR "used by" but not both, you could instead use an expense_type field instead of 2 separate fields).

As a sidenote, I would recommend against using space in field names.