A wireless access point is just a more accurate accurate term for a wireless router.
If you're asking what the Unifi UAP‑AC‑HD is, it's a relatively inexpensive, prosumer, wireless access point from Ubiquiti. The main appeal is: the Unifi ecosystem (optional, but it does offer extra capabilities for your network) and PoE connectivity (ethernet cable is used for data and power). I have two Unifi AC Lites (a slightly less capable model than the HD) in my home they work quite well (and also look good).
On the professional end, Ubiquiti provides wifi hardware for commercial settings like stadiums and conference halls, so they're well versed in creating hardware/software that deals with hundreds or thousands of users/clients. They also offer long-distance communication equipment (think 'wifi' over hundreds of metres)
To be more precise most serious business grade wireless access points such as the Unifi UAP series are not actually routers, they're layer 2 ethernet bridges onto a single switch fabric, or a varied set of VLANs in the case of an AP that broadcasts multiple SSIDs and connects users to different network segments.
The routing is done elsewhere, either at the switch that the AP is plugged into, or something another hop or two upstream of that.
The typical $50-100 "router" with built in 802.11ac wifi that you might buy at best buy is indeed a router, with both wifi, some basic routing/nat ability, and a dedicated WAN interface.
