Actually, neither will currently work, but the second option is closer to what you want to do.

You'll need to use either 'and' or '&&' to conjoin the logical expressions, which must be explicitly stated as you did in the latter code.

if (($STATUS1 =~ m/^Running$/i) && ($STATUS2 =~ m/^Running$/i)) {     
+                         
  print "match\n";           ^^
}
[download]

You could also use:

if (($STATUS1 eq "Running") && ($STATUS2 eq "Running")) {
  print "match\n";
}
[download]

... if you could expect the upper/lower case not to change. You've already tightened it down pretty hard with /^...$/, so a test for equality might also be appropriate.