You can tour with almost anything. The bike type tends to get more specific depending on the load you will carry with you and/or the type of terrain that you intend to ride on.
As an example if you were simply going to ride with a group from one place to another and all of your clothing and gear was going to be carried by a SAG wagon then virtually any reliable feeling bicycle will work fine.
The load gets a bit higher for light touring where you carry bike repair tools and minimal clothing, snacks etc on the bike with the intention of sleeping in motels along the way. Again a road bike would be fine in most cases.
When you get to carrying everything that you need with you then you need a bicycle that can handle your body weight + the weight of the gear + the bike's weight. Some bikes can't handle that kind of load without becoming very squirmy/difficult/flexy to ride. Everyone has a different tolerance level for what's acceptable.
Terrain plays a role too. While I can ride a fully loaded/self-contained touring bike on technical singletrack the bike is not as comfortable to ride on that terrain as is a mountain bike with different handlebars, wider tires etc.
Your original question was about touring with an old ten speed and I haven't forgotten it. The answer is yes you can tour on it depending on the type of tour and your comfort level.
In terms of differences there were a lot of different types of bikes called ten-speeds back then. It's not really a meaningful description. Some 10 speeds were even sport and full-on touring bikes.
What you need to look at are things like the following if you plan to try a fully loaded/self-contained tour:
1) Are there braze-ons to allow you to easily mount rear racks? Some racks have alternatives for bikes without braze-ons but it usually limits the maximum weight that you can carry.
2) Is there enough space between the tire and the frame so that you can mount fenders on the bike? Are there eyelets near the front and rear forks to allow fenders to be mounted?
3) How well does the bike handle when you add weight to it?
4) If you mount a rear rack on the back and place a saddlebag/pannier on it do the heels of your shoes constantly rub on the bags?
I hope that helps.