Many sights in Spain have reduced prices for "Seniors". Does this include senior citizens (70+) from the U.S.?

It wasn't always 60 during my recent trip to Spain, though I don't recall which places used 65.
None of us (mostly US citizens) were asked nationality.

State retirement age in Spain is 65, so discount for 'jubilados' (pensioners) usually applies from 65, unless you are in receipt of disability pension because of ill-health or handicap. You need documentary evidence of that, usually only in Spanish. If you are 65+, just your passport will do.

Ha - About ten years ago my sister and I were in Salamanca. At the time, I was 60 and she was 58. We were paying to go into a tourist site, and the cashier smiled and said, "Jubiladas" and gave us the discounted senior price. I was happy to save a few euros, but my sister, who doesn't speak any Spanish, was confused when she got her change back from the ticket purchase. I explained that we had gotten the senior discount - and she was incensed that the cashier had thought she was over 60! She actually went back and paid the full price. It still makes me laugh when I remember it.

and the angst probably made her look even older.

That's very funny, Dukey.

Unless things have changed recently, the Paradors have their Dias Dorados discount rate which also includes breakfast when any one guest is 55 or more. Passport ID will do - I did this at 55 years and 2 months old with no issues.

The word for senior is jubilado, pronounced who-BEE-lod-oh. You will signs for them at museums, just show your passport.