What's the difference in meaing between a pair of white shoes and a white pair of shoes?

What's the difference in meaing between a pair of new glasses and a new pair of glasses?
No difference. Use either one.
They are wearing the same school tie but a different pair of shoes.

She wore a pair of different shoes, one flat and the other with a high heel.

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I would say

a pair of white shoes (I understand it as white shoes, of which there is a pair.)
a new pair of glasses (I understand it as a pair of glasses, which is new.)

I have no coherent explanation why they seem better to me than the alternatives. Perhaps it's because a shoe is a separate object, but it makes no sense to think of "a glass" of a pair of glasses as a separate object of some kind. But more likely it's the adjective "new", because I would also say a new pair of shoes. Saying them the other way is also acceptable.

new white shoes, not *white new shoes
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 paco2004's reply was promoted to an answer.