A regular expression can tell you two things: Whether there's a match at all, and what some parts in the match are. You are using it in different ways, on two levels:

$row =~  /.*,(.*)/ is a pattern match. It returns whether $row contains the pattern. If you have parentheses in the regex (and you have), then the part of the match within the parentheses is captured - and if you evaluate the pattern match in list context, these captures will be returned as a list. By writing my ($value) you create a list context, therefore you get whatever matched after the last comma.

$row =~ s/,[^,]*$// is a substitution s/text/pattern/. Substitutions change the variable they operate upon, and they return the number of substitutions made, regardless of context. Hence the 1 in the second line: One substitution. You get the substring before the last comma in the variable $row by deleting the last comma and whatever follows it.

If you want the second example to behave like the first, add a capture, and replace the substitution by a match, like this:
my ($val) = ($row =~ /(.*),[^,]*$/);

A good reference for all this, and a lot more, is perlretut.