To boil vegetables, you add the vegetables to a pot of water, and boil the water for a short duration until the vegetables are sufficiently cooked. One may add salt or other flavorings (such as broth, as you mentioned) to the water prior to boiling.
Steamed vegetables are cooked in a steamer basket, where the vegetables are not in the water, but are instead sitting above the water, and are thus cooked by steam.
Salt must be added to steamed vegetables after they are cooked rather than to the water prior to cooking, since salt does not evaporate.
Steamed vegetables can retain more of their original flavor and nutrients, since they do not leech out into the water during boiling. On the other hand, you cannot add additional flavors to your vegetables during steaming--since flavors cannot soak into the vegetables from the water, either.
Which taste/texture you prefer, of course, can be a matter of personal opinion.
In my experience, boiled vegetables are often mistakenly referred to as steamed vegetables. And often, many restaurants will sell "steamed vegetables" which are really just microwaved frozen vegetables, which may strictly be steamed (it certainly isn't boiled!), but really bears little resemblance to the true steaming process (and has relatively poor flavor, as well).