Confusion over dual band routers - Does that mean that it broadcasts both 2.4Ghz and 5Ghz signals at once or that it has the option to broadcast one of the two?

I am looking to buy a new router/modem combo and need one that can broadcast both 2.4GHz and 5GHz signals at once. I live in a large apartment building so 5GHz is critical because there's a lot of interference. But I have a wireless printer, among other devices, that will only connect to 2.4GHz.

I've been doing some research and I see a lot of routers advertising dual band, but I can't find anything specific about whether both signals are broadcasted at once, or if it simply means you have the option to use either. Right now I have the motorola Surfboard sbg6580, and I can switch between the two signals but not use both.

So when a router is advertised as dual band, does that mean that it broadcasts two signals? And is there a router-modem combo that any of you know about that you would recommend for my situation?