beckon, invite, summon, engage
招 centers on calling someone to come or participate: beckoning with a gesture, inviting, summoning, or engaging someone's attention or service.
招 combines 扌 (hand) with 召, which likely contributes both sound and the idea of calling or summoning. The hand radical reinforces the gesture of beckoning.
The hand 扌 beside 召 suggests a hand motion calling someone over. Picture a hand beckoning: 招 is to invite or summon.
For ショウ, imagine a show host beckoning the audience to come closer: show -> ショウ, and the hand gesture invites them in.
invitation
to invite; to ask
call; summons; convening; convocation
invitation; summons; bidding (e.g. to host the Olympics); calling
(courteous) invitation; call
beckoning cat; figure of a cat with one paw raised (usu. white porcelain)
invitee
invitation
beckoning
to invite in; to show someone in
good luck charm; something that encourages or invites good luck
invitation; bringing over
invitation
invocation of the spirits of the dead
unsolicited promotion
requesting the testimony of an unsworn witness (who is not bound by perjury law)
summons to appear before the Diet
to beckon (to); to invite
to beckon
uninvited guest