It must be the case that both m{} and qr{} are *both* pattern matches.

No. Read qr's documentation. It does not perform any matching. It simply compiles a pattern.

Isn't a "pattern match" a "regular expression pattern"?

Matching is the action of checking if something is consistent with a definition.

A pattern is a definition of a set of strings.

Binary "=~" binds a *scalar expression* to a *pattern match*.

Indeed it does. These matching operators are m//, s/// and tr///. If you don't use one of these explicitly, you are using m// implicitly.

$x =~ m//     =>    $x =~ m//
$x =~ s///    =>    $x =~ s///
$x =~ tr///   =>    $x =~ tr///
$x =~ EXPR    ~>    $x =~ do { my $anon = EXPR; m/$anon/ }
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This means that all of the following are functionally equivalent:

$x =~ m/abc/
$x =~ qr/abc/
$x =~ q/abc/
$x =~ qq/abc/
$x =~ qx/echo abc/
$x =~ 'abc'
$x =~ "abc"
$x =~ sub { "abc" }->()
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What it doesn't mean is that all operators perform regex pattern matching. qr/abc/g makes no more sense than qq/abc/g.