Not a lot, when you are referring to time. You can equally well use 'prolong a visit' and 'extend a visit' - the main difference is in the implication that the visit was (or was felt to be) long, if you use 'prolong':
Mother-in-law to daughter: 'Would you mind if I extended my visit for another day or two?
Husband to wife: Do you mean that old bat is going to prolong her stay?
But when you're talking about space, use 'extend': you 'extend a building'.
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