There is a class of problems called decision problems that have an yes/no answer. These problems can be further be classified in decidable, where we have a way to solve them, or undecidable, for which there cannot be or has not been yet discovered a way to solve them.
However, there is another set of problems where we are not interested in a yes/no answer, but rather in a more specific solution. For example, there are optimisation problems, where we are searching for the best value according to some parameters, or counting problems, where we are interested in counting the number of instances where certain property occurs.
To sum it up, decision problems are a specific class of problems, a subset of which can be solved by algorithms. However, algorithms can be used to solve problems in other classes.
Now, given an algorithm for a specific problem, one can solve multiple problems equivalent to the original one (there are ways of "translating" a problem in the terms of another one, and having a solution to one problem means having a solution for all such problems).