If there is a distinction, the method is more abstract (*), while the algorithm is more practical. The algorithm is the series of steps that you go through to get the job done.
Depending on circumstances, the two can be synonymous. It sounds like in your case they more or less are.
Inasmuch as there may be computation involved, this may have its own sub-algorithms.
(*) There is an exception, in that at least one programming language uses (or perhaps mis-uses) the term "method" to designate what other languages call functions, procedures, or subroutines.