In short, a light box is a whole panel backlit evenly so the full face glows, while an LED sign is usually shaped lettering or a logo lit in outline with the wall showing through around it. Both are lit and branded, but they give a different look and suit different jobs.
Choose a light box when you want a full artwork panel: a menu, a poster-style advert, or a big logo on a solid glowing background. A Bespoke LED Standing Light Box is the free-standing version. Choose a shaped sign when you want just your name or logo glowing on its own, which reads as more of a design feature than an information panel.
As a rule of thumb, a busy trade stand needs the information a light box carries, while a bar wall often looks cleaner with a shaped sign. Compare the panels in the LED Lightboxes range, then get a free mock-up.