I am working on a basement bathroom renovation in a basement built in 1969. Fasteners for the firring strips state they are not to be used in cinder block walls, but are OK in concrete block walls. How can I tell what I have?

Concrete masonry unit - Wikipedia, the free encyclopedia

According to this site you should have concrete blocks and not cinder blocks.

Cinder blocks have not been made or used in the USA for some decades. You likely have concrete block which is far stronger. How to tell for sure, try hammering in a cut nail into the block, if it holds tight without breaking the block you have cement.