A protocol and a distributed algorithm are completely different things.
A protocol is defined mechanism for communication that the communicating parties use to exchange information. It is the rules of the language used to carry the information.
An algorithm is a recipe for solving a problem that is made of a sequence of steps to follow that will lead to a solution.
A distributed algorithm is a recipe that uses many parties to contribute to the solution of the problem.
In a distributed algorithm the different parties may need to communicate either with each other or back to some central location where the solution is collected. They will use a communication protocol to achieve that transfer of information, so a distributed algorithm is very likely to use a protocol, but that is not the sole purpose of the protocol and that protocol can be used for many other things besides distributed algorithms.
It is very important not to conflate the two, in the same way that it is essential not to confuse chalk with cheese, otherwise it would be bad for the recipe.