OER and ZTC are often used interchangeably but they are not necessarily the same thing.
A zero textbook cost course is one that uses learning materials that cost the students zero dollars. For example, materials from Western Library's Databases are considered ZTC but not OER. Why? While the learning materials cost the students zero dollars, there is a cost to Western Library in the form of database subscription fees and other material costs.
Adopting Open Educational Resources (OER) is a common method of eliminating textbook costs in courses. OER carry an open license. This is a type of license (Creative Commons - CC) that grants permission to access, re-use and redistribute a work for free, with few or no restrictions.
If you see an open license symbol like the this one, that's how you know it's OER!