I highly doubt the adapter is simultaneous dual band. It is probably only dual band. Most client devices have a single radio that can operate in the 2.4GHz ISM and 5GHz UNII-I/III (sometimes -II as well) bands. Routers/access points usually have a seperate radio for 2.4GHz and one for 5GHz, so they can operate in both bands at the same time.
Some routers/APs do actually let you band the bands together when connecting to a similarly capable router/AP in bridge mode. It is uncommon though even in true concurrent dual band devices to connect to the same device using the same bands.
I guess lucky with my equipment. I can get 180Mbps 2.4GHz with my TP-Link WDR3600 and Intel 7260ac, and it is only 300Mbps "capable". I get 200Mbps on 5GHz (same room ONLY there of course). Just a lil' ole N600 router.
As for the advertising, it is misleading if you don't understand what it means. However, it isn't actually false at all.
It is almost exactly like a vehicle's horsepower rating, if you could see the dyno numbers while you were driving. A typical 200HP car is probably only putting 160HP to the road once you factor in gearing and drive train losses (which are tyically in the 18-25% range depending on the gear box and drive type).
In the case of wireless, you lose a certain percentage to forward error correction, beacon frames, lost packets and a few other things. Of course the further away you are, the lower your SNIR becomes and you drop in link speed.
The best of the best I have seen for link utilization is 224Mbps out of a 300Mbps connection, which translates to ~75% utilization, which doesn't include the fact that a few bits of that are getting taken up by packet headers and stuff, which actually makes utilization probably closer to 80-82% (this was/is with SMB file transfers).
That certainly isn't typical. I've seen other 300Mbps 11n setups barely hit 140Mbps, even when I KNEW there was no source of interference and I was close to the router/AP in question.
Different equipment is going to behave differently, and of course a noisy wifi environment or strong signal attenuation (or worse, both) will and can drastically impact what you can get.