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

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

I agree that the Swan's "no important difference" seems to imply that there might be a minor difference. The Collins Cobuild English Usage (p765), on the other hand, is categorical:

You can talk about a way of doing something or a way to do it. There is no difference in meaning.

It continues:

Note that if you use a possessive with way, you must use 'of' and an 'ing' form after it. You do not use a 'to' infinitive: They are part of the author's way of telling his story.

Why must there be a difference - however slight? It is a difference of grammatical structure, it may be a rhythmic difference, it may be the individual preference of the writer what he prefers, but the meaning is the same.

I've been reading a passage about cryptology.The author used several times a/the way of doing sth and near the end once a way to do. That made me look up on the Internet if there's a difference between the two structures.The previous answers didn't help me at all to make out the difference. Then I read again the passage ( it's from a student's book of an English course) and I'm quite sure I've done.The times when he used a/the way of doing referred to the past, while when used a/the way to do referred to the present/future. For example, he speaks about the ways of sending hidden messages used in the past and a way to send hidden messages ( meaning if you want to, now or in the future )So my opinion is a/the way of doing means the way/ways which have used, the way to do means if you want to do sth this is a way to do.