You are correct that we typically use "the" before the names of rivers but not before the names of waterfalls. For example, we say "the Amazon River" or "the Thames River," but we say "Niagara Falls" or "Victoria Falls" without "the."
There are some exceptions to this rule, however. For example, the name of the waterfall in Yosemite National Park is "Yosemite Falls," which includes "falls" as part of the name. Additionally, some rivers are sometimes referred to without "the" when they are named after a person, such as "Mississippi River" or "Hudson River."
It's important to note that there are always exceptions and regional variations in language use, but the general rule is to use "the" before river names and not before waterfall names.