Allow me to think out loud for a minute. You may want to just skip to the end...
Tag Descriptions:
Networking:
networking
This tag is for any home networks, server clouds, internet problems, repository
issues or server administration.
Internet:
internet
Questions about connecting to the Internet.
Wireless:
wireless
Questions about using wireless connections in Ubuntu.
How Would They Be Used?:
Still thinking out loud. The networking tag to me means exactly what it says; networking. The internet tag is more specific saying it's not just about networking it's about the worlds biggest most famous network the internet. There is also a wireless tag to specify that a connection involves a wireless signal.
So a question tagged networking could be about setting up a home network setup, a question tagged networking and internet might be about getting internet access available over that home network, and a question tagged networking, wireless, and internet might be about setting up a home wifi network that will provide internet access.
How Are They Being Used?:
The next thing to factor in is how are they being used now.
First 3 Questions From Internet:
First 3 Questions From Networking:
First 3 Questions From Wireless:
So it looks like they are being used okay. The internet tag has 1,378 questions, the has wireless tag 6,131 questions, and the networking tag has 5,698 questions. To me this suggests they are all used enough to earn their keep.
What Do The Words Really Mean?
I think it's important to keep in mind what networking really means. It refers to the connection of 2 or more devices in a communicative manner. Here on Askubuntu that connection must be Ubuntu relevant, and follow the restrictions imposed by the tag, which tend to be more computer-networking (linking of computers). The same goes for wireless which if you read the tag's detailed description tells you it's not just for computer-networking (linking of computers) it's for any Ubuntu related use of a wireless signal including keyboards, and mice. Lastly the internet which is a specific global computer network.
My 2 Cents:
Specificity is only useful to a point, and in this case the networking tag doesn't appear to be overwhelmed with questions; the site could easily get by without an internet tag. In summary I see the point in having an internet tag, I would be happy to see it stay, but as a subcategory of networking it is expendable. While I am not for it's removal I would understand if it were.
EDIT 1:
There are several comments discussing 3 postings as examples of using the internet tag, if they should actually be tagged this way, and if merging such questions into the networking tag makes any sense. "Are they actually about networking?", being the argument. Rather than reply to all these comments individually I think it might be more effective to simply share my thoughts through an edit.
Is The Internet Tag Suitable For These Questions?:
Question 1:
Lets set aside what this question is currently tagged as; what could I tag it as? Well firstly we're dealing with a user-network application (an application that uses a network) specifically Mozilla Firefox so the networking tag could be used. The question doesn't state internet usage is involved, but the OP did have it tagged with internet so we can assume Mozilla Firefox will be used online. Remember web browsers while commonly used for internet sites they not restricted to such, and can just as easily be used for intranet sites. A web browser is a viewer for served documents/applications so some form of networking is required. Since the OP seems to be intending internet usage the internet tag would work. As mentioned before this question is about Mozilla Firefox so the firefox tag would make sense. This question could be tagged networkingfirefoxinternet. In this case networking is the primary tag with firefox and internet as sub-category tags. Keep in mind of course that there are a mass of available tags which means it is often possible to effectively tag a question in more than one way. There is also tag limit, and even within that limit it possible to over-tag a post (or as I like to call it "tagging-to-death"). In this question the usage of one or both the internet tag and networking tag works. Would the post work without them? Yes. In this case the question is about Mozilla Firefox, and the firefox tag works nicely as either a sub-category tag, or a primary tag. Due to this another effective way of tagging the question would be to use firefox tag as the primary tag, and then browser tag. Keep in mind that firefox tag also works nicely as a sub-category of other tags like software-recommendation. I feel this question is an acceptable example of using the internet tag. Some ways I could see tagging this question:
Question 2:
What could I tag this as? Well we're dealing with Apt so the tag apt is a good fit. Apt is a program for retrieving and installing Debian software packages. This question is a great example of the use of the internet tag because Apt doesn't require an internet connection, or even a network connection. You can use it with local repositories that don't involve networking at all. So you could simply tag this with apt and leave it at that especially if you're only dealing with a local repository. However in this question the user has specified they will be using online repositories so both the networking and internet tags work very well here. However as mentioned before there is a mass of available tags, and it is possible to effectively tag a question in more than one way. It's also possible to over-tag a post. In this question the OP is getting internet via a mobile ISP provider so the wireless tag could also be helpful. I can see there are a few different ways to effectively tag this question:
Question 3:
For now lets set aside for a moment that this question is about Mozilla Firefox and Chromium, and just pretend it's about Mozilla Firefox. As before this means tags networking,firefox, and internet would all work, but of course that isn't the only way to tag the question. Now this question is about a sub-topic of Mozilla Firefox; privacy, it's also about Chromium, and the basic principles will apply to almost all browsers. This question therefore makes a good example of a one that could tagged with internet and networking, but might be more effective tagged as something else, because it has so many other more specific tags that can be used for it. Since it discusses two browsers their tags would be a good start. The following seem to be good fits, but because the OP mentions 2 specific applications the first would be more ideal:
What Are My Thoughts On All Of This?:
I think that all 3 questions work fine with the internet tag, this doesn't mean they need to be tagged with it, or that their aren't other tags which would work. In some cases other tags may even work better. As far as merging the questions currently tagged internet into networking I see no problem; they are networking related. The reason these questions seem to be the topic of debate is because they are about user-network applications (an application that uses a network), rather than administrative-network applications (an application that manages, secures, or provides information about a network). As well as because of how networking tag is currently described. If a merge does occur I think some manual re-tagging is a good idea, because some questions have better tags available.