MultiFunction Network/WiFi Devices:

It is commonplace to combine two or more of the individual functions described above into a single box. When manufacturers do this, the functional lines often overlap or blur, resulting in the possibility of confusion when they choose names for the resulting equipment. Unfortunately, manufacturers tend to use the simple term "Router" for most of these combinations, so you'll need to study the published details to figure out the exact combination they are offering. A careful reading of the retail packaging is generally sufficient. Here are some of the combinations in common use today:

Router and Ethernet Switch combinedRouter and Ethernet Switch: Almost all consumer-grade routers today include an Ethernet Switch with 4 or more Ethernet connectors. Thus, at the back of the router, you'll generally see 5 Ethernet jacks. One will be labeled separately, and it will reference an "Internet" or "Internet-Facing" or "Upstream" or "Wide Area" connection. Connect that to your Broadband modem. The others will be grouped together, and an associated label will reference "LAN" or "Local" or "Downstream" connections. Use Ethernet cables to connect those to one or more PCs, printers, etc. Manufacturers will almost always use the name "Router" to describe this combination, and the general expectation is that any basic router will include a basic Ethernet Switch.

Router, Switch, and Access Point combinedRouter, Ethernet Switch, and Wireless Access Point: This combination is the same as "Router and Ethernet Switch", but it adds a Wireless Access Point so that you can connect one or more computers via WiFi in addition to those connected with Ethernet. You can use any practical combination of Ethernet and/or WiFi connections. Manufacturers generally use the name "WiFi Router" to describe this combination. It is also possible to bypass the Router portion of this kind of equipment, if you only need Ethernet Switch and/or Wireless Access Point.

Modem, Router, and Switch combinedModem, Router, and Switch: If you obtain your basic router from your Internet Service Provider, it will probably include modem logic that's compatible with their DSL or Cable connection. Like other routers, this logic almost always includes a  4-port Ethernet Switch, so you can connect it with 4 computers before you'll need to expand your Ethernet LAN subnet. This combination doesn't include a Wireless Access point, so every connection will be wired. Manufacturers are split on the name of this combination: sometimes they call it a "Broadband Modem", and sometimes they call it a "Router". Sometimes they call it a "Residential Gateway".

Modem, Router, Switch, and Access Point combinedModem, Router, Ethernet Switch, and Wireless Access Point: If you pay a premium to your Internet Service Provider you can get this all-inclusive combination. The modem logic will be compatible with the particular broadband technology supported by your ISP (DSL or Coaxial Cable). The Router will create a new IP subnet on which you can share your single Internet Address with several computers. The Ethernet Switch will expand that new subnet with several physical Ethernet connectors for wired PCs, and the Wireless Access Point will allow shared radio access to the resulting LAN segment. You can also buy these devices from retailers, but be sure to check the specs on the modem. Some support Cable only, some support DSL only, and some support both. Most manufacturers describe this combination as a "WiFi Router". Sometimes they call it a "Wireless Residential Gateway".