There are two kinds of invitations to formal functions which, unless time is short, are prepared on cards engraved in script from a copperplate:
Formal Private Functions
Formal occasions, such as luncheon and dinner parties
At Home invitations for all other parties, such as receptions, garden parties, luncheons, dinners and suppers
Informal Private Functions
Invitations to informal functions may be extended by letter, telephone or email.
It is up to the hosts to decide, and make clear to guests, the appropriate level of formality and all the other relevant details and arrangements.
The level of formality of the invitation should accord with that of the occasion.