Wireless devices: can modems be built-in into routers?

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After taking a look at my router's configuration the other day, I noticed for the first time that the router's page had a section called modem in it where I can configure DHCP, DynDNS, etc. I have some trouble figuring out identifying how my network works at home. I can't seem to find any box which looks like a modem. So I have a few questions:

1. If I can access the modem's configuration on my router's page, does that mean that the modem is inside the router? Is that even possible?

2. I have posted pictures below of two devices I have at home whose function I know little about. The first one (TPLink device) has a blue RJ45 cable coming out of it and plugs directly into my router. What's this device called and what does it do? The second pictures is a device which plugs into an outlet and from which comes out a RJ11-connected cable that plugs into the DSL port of my router. What's the name of the device with the 6 holes into it? Can we call that a telephone outlet? From what I could understand, here we have cable for TV and DSL for Internet access. I just want to understand what type of Internet connection I'm dealing with here and how all of that is connected together.

@thomas-pondant,

From what I can see, the device you show is your DSL modem. On the modem configure of your wireless router, it's so that your provider can set a PPPoE password if needed to connect to the DSL network.

That 6 hole adapter may have been for a time, when the home was wired for pulse dialing or rotary dialing phone but your line has been adapted for the RJ-11 connector instead.

Thanks Ronnie, already much clearer now! I don't understand though why my provider would need to connect to the DSL network. Do you mean that a technician could possibly use that by connecting to my router's page at my home to make a connection to the provider's network? Do they need that to troubleshoot a home network for example? And do they have access to my router's page outside of my home or would they have to be in the house connected to the network in some way to do that?

I hope my questions are not too confusing!

@thomas-pondant,

The provider wouldn't be accessing your equipment. But for you to configure it to allow for access to the DSL network. You may or not may not need to configure your wireless router to access the DSL network. The modem is normally their demarc, separating the customer's edge from the provider network. But for you to have access and now allow everyone to just jack into your RJ-11 outlet and get access to DSL, you may have to provide this PPPoE (or you may see PPPoDSL) password or id, etc.) for access.

Any troubleshooting they would do is only up to the Demarc on their end and the rest is your responsibility.