Router vs access point

Solution 1:

Yes, from an IEEE 802.11 ("Wi-Fi") protocol perspective, these products are both Access Points. The 802.11 standard doesn't define whether the AP should act as a simple bridge to Ethernet, or a router to an IP network, or a NAT gateway, or anything else.

In modern marketing of these kinds of devices, the marketing people tend to sell it as a "wireless router" if it has home gateway features like being a NAT gateway and a DHCP server, and they tend to sell it as an "AP" if it's just a simple bridge.

However, devices that marketers sell as APs tend to have features important for business and other institutional networks, such as PoE, mass manageability, advanced diagnostics, and more.

Because there's not as much market for these business-oriented boxes, the economics of the market are different, causing these business APs to sell for more than a very mass-market competitive consumer-focused home gateway wireless router box with generally the same top-level specs.

In this particular case, you'd buy this AP if you needed to power it over PoE. Most people don't need PoE, so the people that DO need it end up paying a little more for it because it's a relatively rare requirement.

Solution 2:

You can use most typical Small Office / Home Office (SoHo) routers as access points. Just don't use their WAN port, disable their DHCP server, and assign them an IP address inside your LAN but outside the other router's DHCP range. Configure the WiFi however you want, but using the same SSID and encryption is recommended to allow roaming and using different channels is recommended for improved performance.