I've been looking through dictionaries trying to corroborate my personal (UK-based) understanding of these terms.
Both certainly imply a degree of prosperity, but neither I think imply that person is very rich; say millionaires not billionaires.
I would agree with FumbleFingers that both are somewhat colloquial, and that well-to-do is rather dated; the biography of P.L.Travers (the author of Mary Poppins) describes her remembering her father as well-to-do.
I have always though of well-off as describing the financial status of a person. The Free Dictionary says moderately rich.
On the other hand I have thought of well-to-do being as much concerned with the outward behaviour arising from that wealth. Such a person not only has money but uses it to buy possessions, often those that increase their social standing.
The Collins dictionary gives this example:
In the seat in front of him a well-to-do matron and her paunchy husband were busy adjusting an expensive camcorder.
Pacter, Trudi YELLOW BIRD
Note that the matron (woman) herself is described as well-to-do, and we immediately think of someone very well dressed.
This distinction is not clear in the dictionaries I have consulted, but I do think is implicit in the actual terms themselves. It would not, in my opinion, give the same impression to say
a well-off matron