infinitives - Is there a difference between "way of doing something" and "way to do something"?

Is there a difference between "way of doing something" and "way to do something"?

It is on purpose that I did not write "a way of doing something" or "the way of doing something" and "a way to do something" or "the way to do something"… because I feel this is where the answer lies.

Michael Swan's Practical English Usage (third edition, page 607) reads:

After way (meaning 'method/manner') we can use an infinitive structure or of … ing. There is no important difference between the two structures. There is no way to prove / of proving that he was stealing.

I, on the other hand, think there must be a difference, however slight… !

Answer

My impression is that 'the way of doing' tends to be descriptive - i.e., a description of the current state or practice of doing something, whereas 'the way to do something' is prescriptive; there tends to be an insinuation that the listener had better do it that way.

"This is the way to do it" == Do it this way!

"This is the way of doing it" == This is how we do it. You are welcome to try another!

Apart from that 'of doing it', may be the only option when 'way' is qualified by a possessive(my/your) or by a demonstrative adjective(this/that).