Invitations should be sent from whoever is acting as host for the wedding.

If the bride and groom are acting as hosts, the invitation would read:

Bride’s full name
&
Groom’s full name
request the pleasure of your company
at their marriage
or
are delighted to invite
...........................................................
to our wedding
or
Please join us as we
Bride’s full name & Groom’s full name
join our lives in marriage

or

Please share with us a day of great happiness when
Bride's name
&
Groom's name
join hands in marriage on
(Date)
in a ceremony to be held at
(Venue)
on
(Date)
Celebrations will follow at
(Venue)
at
(Time)
RSVP

A standard invitation with the bride’s parents as hosts reads:

(brides parents names)
request the pleasure of your company
at the marriage of their daughter
Bride
to
Mr Groom’s full name
at
(ceremony venue)
on
Date
at
Time.
Reception following at
(reception venue).
RSVP
(date, address, phone etc)

When divorced parents give the wedding together,
invitations can be issued by both parents.
If the bride’s mother has remarried and the invitation is issued jointly,
it is worded:

(bride’s mother)
&
(bride’s father)
request the pleasure of your company

If the bride’s father has died and her mother has remarried,
the bride’s surname should appear on the invitation:

Mr and Mrs (remarried surname)
request the pleasure of your company
at the marriage of her daughter

It is possible for the the invitation to be sent by both sets of parents:

(bride’s parents)
and
(groom’s parents)
request the pleasure of your company
at the marriage of