Yes, you can offer both!
You can issue as many discount codes as desired for any event. They can be restricted by expiration date or # of codes redeemed. Intelligent promoters use discount codes to measure the success of marketing & particular sales outlets.
You can also offer vouchers & gift cards that can be used for a single event or all the events in your company's box office.
You can instruct us to create your discount codes & vouchers when you setup your event ticketing, or if you desire to create codes later, you can open a support ticket with your request.