You can tour on any kind of a bicycle, or a unicycle if you like. You can cross a continent on a one speed Huffy you got for $25.00 in a Salvation Army thrift shop. Different kinds of bikes are built for different purposes; not that their uses cannot overlap, for they can and do. When I bought my first touring bike I did a lot of reading about cycling beforehand. I looked up exactly what was meant by touring bike. I got a bike that fit the specifications. It was quite noticeably more efficient than a cheaper bike I already had. The touring bike is longer, it has fittings for racks and fenders, and it is more forgiving of the inevitable creases and bumps and holes you will find in your road. A hybrid is ok for touring. The trail bikes with the wide tires can be used for touring. Many people have toured on such bikes. They are just not meant for over the road long distance touring. Road bikes can be used for touring too. They may be a bit more rigid than touring bikes with a shorter chassis. You could probably even tour on a racing bike, but you might want to keep your load weight down, and I would not suggest it. There was this one guy who had a bike built from three or four different frames. He was up quite high in his seat, and he pedaled this contraption backwards across the United States, so there you go.
In my opinion, if you want to go on a long tour by bicycle over the road, you should use a touring bike. It looks like a racing bike with the drop handlebars, but is longer, heavier, stronger, and might have tube angles set different from a racer, and it is less rigid than a racing bike. This bike was made especially for the long distance touring bicyclist. If you have the proper fit between the bike and your bodily proportions, and if you have the right saddle, you are ready to go.
I have done many long tours with touring bikes, and only two with lower-grade mountain type bikes. I would not tour again on a mountain bike.
In general, the only rule is there is no rule. Well, except for having a good time and enjoying it, if you can.