Anyone who calls a Domain Name an "Internet Address" probably doesn't know very much about either...
Prepare to lose on this one.
Take "broadband"... What is the antonym of "broadband"?
Why "narrowband", of course! Except according to the (unfortunately false) doctrine that the meaning of a word belongs to the community that coins it, the antonym of "broadband" ought to be "baseband". The "base" in "baseband" refers to zero hertz; a band that includes 0 Hz is the baseband in any kind of signal encoding scheme.
In our alternate world ruled by engineers, "broadband" refers to a signal that does not have to include 0Hz, and which thus can be frequency multiplexed on media such as coaxial cable or fiber optics. This allows us to make use of that medium's full transmission capacity, which means we can serve more people with greater transmission bandwidth.
The simplicity and precision of this way of using language warms my engineer's heart. A layer 1 signalling scheme that can be frequency shifted for multiplexing is "broadband"; one that cannot is "baseband". If you want to tell me a service is "fast", give me a number and a unit so I know whether you're talking throughput or latency.
But you can't expect people trained in marketing (whom I have nothing against by the way) to use language with this kind of beautiful precision. Marketers deal in imprecision, and like it or not they have much, much more influence on the direction of language than we do.
As soon as marketers wrapped their brains around "broadband" implying higher throughput on a shared medium, the term was pretty much destined, not just to lose its virginal purity, but to become their property as language pimps.
DNS exists so ordinary people don't have to deal with actual Internet addresses. It makes Internet Protocol invisible to them, so as far as they're concerned the term "Internet Address" is up for grabs. I always assume when someone who is not a techie says "Internet Address" he's talking about a domain name or URL.