I'm seeing routers and adapters labeled as say 300+300 or N600 for example.
Does that mean that if both ends have this config that it will actually use both frequency bands at the same time to achieve higher speeds? Or is it just more marketing speak and they only use one band or the other at a time?
Almost all clients are not concurrent dual band. Most routers and access points these days are concurrent dual band. That means that the routers and access points can have clients connected on both 2.4 and 5GHz and potentially hit those numbers of say 600Mbps, but the clients never will, even if the client is dual radio and 2.4+5GHz capable.
There are a small handful of bridges, routers and access points that support high speed wireless bridging where they can bridge a wired connection using both bands at the same time with another bridge/router/access point that supports the same thing. I just am not aware of a single client that can connect on both bands simultaneously.
Also keep in mind, the 600Mbps is RAW rate of both bands combined, not the actual data payload rate. On 11n you lose about 40% to overhead and data correction making the absolute MAXIMUM possible speed about 60% of the stated. That is with a really good client and router, close to each other with no interference.
For example, I have an N300 router and I see around 180Mbps absolute max on my laptop (Intel 7260AC card in it, no competing networks, close to the router).
5GHz 11n versus 2.4GHz 11n tends to be a little faster if you are close to the router, but that is a combination of 5GHz radios tending to be a little better, fewer competing/interfering wifi networks and fewer interfering devices (IE wireless phones, microwaves, other potential emitters). Still roughly the same max speed after overhead.