Why might researchers distinguish their interests between applied math and computational math?
"Applied" math is in opposition to "pure" mathematics: that is, applied mathematics is used for a specific ("real-world") problem, such as fluid mechanics, statistical physics, or even the biosciences. This need not be computational: in many cases, it involves the study of differential equations and other analytical tools (expansions and other techniques). 

In contrast, "computational" mathematics implies mathematics that cannot be solved by "pen and paper" techniques but instead require the use of a computer—either desktop or cluster—to solve.