What is the difference between a roomer/boarder and a roommate (RELATED) in IPUMS USA post 2006 ACS?

Relevant questionaire text is as follows:

If a person is not related to Person 1, mark the applicable box. A “Roomer or boarder” is someone who occupies room(s) and makes cash or non-cash payment(s). A “Housemate or roommate” is someone sharing the house/apartment (but who is not romantically involved) with Person 1. An “Unmarried partner,” also known as a domestic partner, is a person who shares a close personal relationship with Person 1. A “Foster child” is someone under the age of 21 who is involved in the formal foster care system. For all other people who are not related to person 1, mark the “Other nonrelative” box.

At first I assumed a roomer or boarder would be someone who makes payment to the head of household who is an owner, but this does not seem to be the case. Roomer/boarders are present in renter households.

The ACS Subject Definitions (see page 78) provides some key insight into the difference between Roomer/Boarder and Housemate/Roommate. According to this documentation (which is from the 2016 ACS):

A roomer or boarder is a person who lives in a room in the household of the householder. Some sort of cash or noncash payment (e.g., chores) is usually made for their living accommodations.

A housemate or roommate is a person age 15 years old and over, who is not related to the householder, and who shares living quarters primarily in order to share expenses.

As you noted, there are instances where roomers/boarders are present in housing units that are rented. However, keep in mind that a roomer/boarder may make a payment to the householder, who may not be the owner of the housing unit.