While we’re being timely, in addition to “jab,” Gigi Simeone mentioned that she had come across U.S. writers/speakers using “care home,” where normally, she said, Americans would say “nursing home.”
I wasn’t aware of ever encountering “care home” in a source from any nationality, so I looked it up in the OED, which has a “Draft Addition” listing as of 2011: “a small institution providing residential accommodation with health or social services for the elderly, vulnerable children, the infirm, etc.” That’s a more general definition than the American “nursing home,” where the residents would be elderly and not the other categories. The most recent OED citation, from the British author Christine Reddall in 2009, is: “When an elderly person goes into a care home, much of their independence and choice is lost.”
The Corpus of Global Web-Based English, which provides a snapshot of the use of the language in 2012 and 2013, establishes that “care home” was, at least in that moment, a Britishism. “Per mil” indicates the times “care home” comes up per million words.
It’s a little trickier to determine whether “care home” has migrated to these shores. I found a few uses in American sources, but they were a bit ambiguous. A New York Times obituary of the poet Diana di Prima said she “had been living at an elder care home since 2017.” In Britain, presumably, the word “elder” would have been superfluous. A June 2020 report on NPR attributed to an official of “a group that represents people with intellectual and developmental disabilities” a statement the effect that “there are consequences to paying less attention to people who live in other care home settings.” But the “other” suggests a broader meaning for “care home.”
I finally found what appeared to be an American “care home”=”nursing home.” A Wired article posted in December 2020 talked about local U.S. health departments sending “extra help in certain cases, such as at a care home or to an infected health care worker.” Unfortunately, when I clicked on the name of the writer, Tom Simonite, I learned that he “received a bachelor’s degree from the University of Cambridge and a master’s from Imperial College London.”
So for the time being “care home” remains On the Radar.
notoneoffbritishisms.com 
Both terms are used in the UK, but nursing homes are for those whose medical needs require support by qualified nurses, for example to dispense controlled drugs or provide certain treatments. These residents will often be funded (wholly or partially) by the NHS. Care homes are primarily for elderly residents requiring just carer support, but may also be certified to include some residents needing nursing care with the proportionate number of nursing staff.
I agree: nursing homes have nurses on site and care homes have carers. As a blanket term in general use, though, care home seems to have replaced nursing home over the last couple of decades. This maybe because of the vast increase in the number of them as a result of corporations seeing a good profit in an ageing population: rates are extortionate and appear designed to wipe out the assets of the elderly before they can pass them on to family. There again, in less capitalist societies the family may care for the elderly themselves. That may be the trade off: farm out the care of the old folk but lose the inheritance. Sorry, didn’t intend to go on a rant!
We use ‘nursing home’ here as well, if it specifically has nursing care. ‘Care home’ is probably more of a blanket phrase for all types of communal residential homes for the elderly, whether involving nursing care or not. And I think the UK is definitely picking up the US model of ‘retirement villages’, which may or may not also have a care home on site. For other groups, such the disabled, I’d probably be more likely just to call it ‘a home’.
Also, “jabs” in Scotland are regularly referred to as “jags” as they are jaggy!
In the UK, when I was a youth in the 60’s and early 70’s, Nursing Home still had connotations of new mothers recuperating from childbirth (10 days Nursing Care was the standard until the late 70’s, I believe).
The Alexandra Nursing Home in Plymouth, Devon (where I was born in 1956) finally closed in late 1985, transferrring the last of it’s new mothers to Freedom Fields Hospital.
And about that time, the term I remember being used for what we’d now call a care home was an old people’s home.
In the US, the terms “care facility” and “assisted living facility” are more common than “care home”.
My dad lived in an Assisted Living Facility, but it wasn’t (in UK terms) a care home, because it consisted of a number of individual apartments (along with a communal dining room and chapel). In the UK, in my experience, a “home” indicates a facility where everything is communal except bedrooms (which may be ensuite).
I feel like “elder care” is a current Americanism, and that the case of “elder care home” more likely derives from this than from the British “care home.”