"As to" is used significantly less than "as for," and they don't necessarily mean the same thing. According to the Merriam-Webster dictionary, "as to" can be defined as:
The first of these is more frequently used than the second. Being a native English speaker, I don't recognize any difference between "as for" and "as to," but they are used in different kinds of sentences. "As for" is often used to either start a sentence or add onto a sentence:
"My wife and I are well. As for our work, it is not going well."
It can also be used (formally) to connote similarity:
"For Hawthorne, as for Borges, his writing was a reaction to his cultural situation."
As to, on the other hand, can be used in the ways stated at the beginning:
"The programmers were at a loss as to how to explain the error."
"The blocks were graded as to size and color."
"Regarding" would not typically be substituted for "as for" or "as to":
"As for the mayor, he can pay for his own dinner."
-> "Regarding the mayor, he can pay for his own dinner."
While grammatically correct, that sentence is a rather atypical form, so "as for" would still be more appropriate. However, "as for" can be defined as "regarding," even though the words aren't very interchangeable in common English. "Concerning" would be slightly more appropriate (though "as for" still sounds better):
-> "Concerning the mayor, he can pay for his own dinner."
Finally, "as regards"/"as respects" is another way of saying "in regard to" or "as compared to."
I hope that answers your question, but comment if I need to explain something better.