Inivitar means invite, of course, but in the right context it can mean treat someone to something. Let’s look at some examples.
- Yo invito. Yo te invito. I’m paying (for us).
- No importa, yo invito. You don’t have money on you? No problem, I got it. My treat.
- Los invito a cenar. Dinner’s on me. Note that the recipients, the people being treated, appear as the direct object.
- ¿Le puedo invitar una copa? Can I buy you a drink? Here, since the direct object is the thing being paid for, the recipient goes in the indirect object position.
The saying El que invita, paga emphasizes the relationship between these two meanings of invitar. If someone invites you to do an activity and uses the verb invitar, it is likely that they are planning to pay for the both of you. ¿Te puedo invitar al cine el sábado? However, if they say something like ¿Quieres ir al cine?, they may or may not be intended to treat you.
Invitar, like mochar, can be used to ask someone to share. ¿Me invitas? Could I share your drink? I was asked this at home; no question of who would pay was involved.
The verb disparar works informally for this same function: Te disparo unos tacos. Let me take you out for tacos. I’m paying.
The usual meaning of disparar is shoot (with a gun), but note that it takes an indirect object pronoun: Le dispararon. They shot him. If you’re expecting a direct object here, it may help to imagine the translation as They shot bullets into him. The bullets are the things being shot (out of the gun). The person shot is the recipient, so they are rendered as an indirect object in Spanish.