Is it clear and natural to say "Both sentence_A and sentence_B change the meaning"?

Question

Note: This post is focused on the use of "change the meaning".

From an ELL post

The trick is that a location/event is often a purpose; your purpose is to go to that location/event. With verbs ("to wear to run"), the trick is that some words can be both verbs or nouns (e.g. run as a noun is an event of running). In these cases, both may be grammatical, but slightly change the meaning.

...

You must wear a hat for gardening ... You must wear a hat to gardening

Rewording it gets

Both "You must wear a hat for gardening" and "You must wear a hat to gardening" may be grammatical, but slightly change the meaning

I understand what it means though, the sentence above itself doesn't seem clear or natural.

I've gone through the top pages linked to Ngram Viewer and didn't find similar use.

The better version could be

Both ... may be grammatically correct, but might have some nuances in meaning.

or

Both ... may be grammatically correct, though the substitution of the preposition slightly changes the meaning

Is my understanding correct?

Answer 1

Yes it does.

You must wear a hat for gardening
means that you must wear a hat when you work in a garden.

You must wear a hat to gardening
is an unusual way of putting things but presumably means that you must wear a hat when you got to gardening functions/classes/events

It's a bit like saying: You must take your gloves to boxing, referring to boxing training/matches/bouts