For the OP (original poster), take a look at this AllDeaf thread:
http://www.alldeaf.com/deaf-product...n-use-pc-webcam-call-deaf-hoh-vrs-number.html
That is the best way, currently, for someone who is hearing to make a point-to-point video call to a VRS videophone.
Your grandmother has a VP200 though, which cannot do H.264 to anything that doesn't pretend to be another sorenson videophone. If you can convince her to get the nTouch upgrade from Sorenson, that will make it possible to follow the above instructions and call your grandmother.
As to the rest of of this silly discussion of what is a modem, and what is a router...
First, a quick primer on "layer 1":
The ethernet you are used to is considered "baseband" with carrier sense multiple access with collision detection (CSMA/CD). Think of it as a wire that anyone can transmit digital data at any time. Before transmitting, looking at the signal on the wire we can see if it is busy or not at any given moment and if we should wait our turn to talk. When more than one person tries to transmit accidentally at the same time, a collision is detected, and the transmitters randomly back-off for an increasing amount of time any try again.
There are real electrical limits to the length of a wire that can be used for digital baseband like this, however. A raw digitally encoded signal quickly distorts and becomes unusable at long distances. In order to deal with longer distances and interference along a longer wire from various sources, we need to encode our digital signals using analog "symbols" that can be differentiated easier at the other end. This is where modulation/demodulation come into play.
A modem is a modulator/demodulator. Anything that encodes a square wave digital circuit into an analog signal for transmission is technically a modem. That being said, the word "modem" has typically meant "something I hook up to my phone line", though the cable providers have embraced it to mean "something I hook up to my coax". If you talk about a "modem" with regard to your ONT, while you are technically correct, it gets people emotionally charged because of differences of opinion on what a "modem" is.
On a phone line, a classical modem encodes a digital signal in an analog manner on copper pair over a plain-old telephone service (POTS) line using amplitude shift keying (ASK), frequency shift keying (FSK), phase-shift keying (PSK), etc. This analog audio is encoded yet again by a line card on your local central office switch as an 8khz mulaw 64k digital channel, and is decoded yet again into an analog audio stream by the receiving party.
By removing the load coil on the phone line and using more advanced encodings like orthogonal frequency division multiplexing (ofdm) and quadrature amplitude modulation (QAM), with line cards on the carrier switch on the other side of your copper pair, Digital Subscriber Line (DSL) connections are technically modems as well. From there, the DSLAM routes the network packets.
Cable providers use 75 ohm coax connections to a head-end as channelized "broadband". Each channel has a frequency range on the broadband medium to modulate an analog signal. Technically, these are modems as well, using QAM16, QAM64, etc.
As a next step along that path, Cable providers have actually moved toward hybrid fiber-coax networks, where the fiber is run to a neighborhood and coax is run from there to the houses.
The newest physical plant is fiber to the home (FTTH) where a house gets an Optical Network Termination (ONT) device. The lasers used to transmit an analog optical wave at fixed frequencies transmits the digital data using symbols as the modems do above, OFDM, QAM64, etc.
With Dense Wave Division Multiplexing (DWDM) there are actually multiple lasers transmitting separate "channels" over the same optical path at the same time without overlapping or interfering.
A repeater is a network device that regenerates a layer 1 signal on a physical interconnect. Simple repeaters are "lossy" and simply boost signal. More expensive repeaters actually use two layer 1 network interfaces and regenerate the signal entirely to boost the distance with minimal loss/interference.
A bridge is a network device that relays layer 2 network traffic. This means that it has two layer 1 network interfaces, and looks at the framed lower level network packets when receiving/sending them between the network interfaces. Bridges relay packets from any port to all other ports.
A "switch" in ethernet parlance is a network device with many network interfaces that learn the layer 2 network addresses of network devices to smartly relay packets only along to the appropriate unicast address of the destination (only relay packets from one port to another port, when possible). Switches are also capable of picking up network loops (when someone plugs a cable between two ports on the switch) byt using things like 802.1d spanning tree. Moderns switches are also capable of supporting many layer 2 segments (grouping together different layer 2 networks across a number of ports) using things like 802.1q VLAN tagging.
A router is a network device that routes layer 3 network traffic (typically IP, as there really isn't a need to talk about OSI anymore). If you have different layer 2 networks on either side of a router, and the router is relaying layer 3 network traffic, it is a router.
That being said, many things are sold as a "router", particularly to residential customers. Like "modem", it has been used to describe everything from a set-top box, to a MOCA/wireless bridge. Anything that "plugs into the internet" is typically called a "router", whether it is really acting as a router or not.
If you feel passionately about properly educating folks about the true meanings of the words they use, please feel free to do so! But, at the same time, understand that the very providers that these folks are calling for customer support are often misrepresenting the very things you are attempting to educate people about. They aren't trying to be difficult, they are merely repeating what they have been told. Take the time to gently educate, and try not to take it out on them.
