That is generally what the powers that be are saying and is probably true. I think it would be difficult to tell exactly how different the age profile is from the first wave since back then you were only tested if you were ill enough to go to hospital. You were more likely to be in that position if you were older so that would skew the positive test figures for that period towards older people. Younger people may have had the virus but generally weren't ill enough to be tested.
I hope you're right about the care homes.