apoc.do.when() is similar to an if/else conditional based on a single evaluated boolean expression, so there can be only two outcomes, with the ability to supply a Cypher query to execute in each of those two cases.
apoc.do.case() is more similar to a case statement, in that you can have several boolean conditions to evaluate, executing the Cypher associated with only the first one that evaluates to true (or falling back on the else conditional if none of the evaluated conditions is true).
