Read the forum guidelines
I currently have residential digital phone service through Cox. I'm not happy with my current phone setup and have been looking at some of the Cisco IP models for my work-from-home office. Can I plug a Cisco IP or VoIP phone directly into the Cox digital phone modem or are these different technologies
Cisco phones in particular can be complex. See Cisco forum post here for some background of a basic setup.
If you get an IP phone, you won't need a digital phone modem. You wouldn't even need Cox Telephone Service.
Technically, your current digital phone modem (eMTA) is an Analog Telephone Adapter. It allows your analog phone to work on a digital network. It converts analog signals to digital. IP phones have an Analog Telephone Adapter inside its enclosure. That's way...among other things...IP phones cost more: more Intel Inside.
Of course, you'll need an IP phone provider to give your IP phone an identify. People would need to dial something.
This is not something that you can handle by yourself per se. This requires a lot more networking equipment and configurations, all of which have to be done by the ISP (Cox). While I am sure they are using a IP phone setup in their business offices, this isn't something that can be easily delivered to their customers' endpoints. The marriage of POTS and IP Phone over Coax is something that is out of my expertise but as Bruce mentioned, Cox would have to have a way of assigning your IP phone an identity (aka phone number) that could be accessed from any telephone in the world just like your current phone number currently is. Plus, that would reduce their income substantially (everyone would dump the phone service). Furthermore, I am not sure how e911 would work and they couldn't offer IP phone service (for free) without being able to get 911 service to work. Its actually more complicated than you think.
However, you could look into a Cisco softphone. I use a Cisco softphone which connects back to my employer. A softphone is simply a software application I run on my PC which is connected to my employer via a VPN. Then I use a regular PC headset and I can dial anywhere in the world, including phone numbers that are otherwise associated with traditional POTS service such as those from a local telephone company.
Unless you subscribe to their business plan and IP phone service, Cox would have nothing to do with a residential IP phone. It's easy to setup; however, on a residential plan, your QoS may suffer. For example, if you occasionally...or frequently...suffer Internet latency or congestion, your voice service would be poor. Business plans normally have more bandwidth and redundancy than a residential plan. I'm not implying IP phones and residential plans don't mix, but you'll need to be vigilant of your bandwidth.
It's easy to setup because after buying an IP phone, you only need to subscribe to a VoIP phone service-provider. The provider creates your account, assigns a telephone number and routes your packets. The provider may also register you for 911. "Oh, you live in Bismark, ND? We'll route 911 to the Bismark 911 Center."
Your softphone example is basically the same as Google Voice. Google sets up and maintains the call and sends voice packets to your PC. If you receive a Google call on your landline, the caller ID displays San Francisco...not the location of your PC.