The \\B in the string literal becomes \B in the resulting string.

In a regex pattern, \B means "Match except at a word boundary".

Since the \B is between an "A" and the end of the string in the first snippet, it's on a word boundary.

Since the \B is between a space and the end of the string in the second snippet, it's not on a word boundary.

You want

$pat = "A\\\\B";
$text = /$pat/
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$pat = qr/A\\B/;
$text = /$pat/
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$substr = "A\\B";
$text = /\Q$substr\E/
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But: \B Match except at word boundary

There are plenty of non-wordboundaries in your string, so it matches when there is no A required.

Use $x = qr/A\\B/ instead.

use YAPE::Regex::Explain;
print YAPE::Regex::Explain->new("A\\B")->explain;
__END__
The regular expression:

(?-imsx:A\B)

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  A                        'A'
----------------------------------------------------------------------
  \B                       the boundary between two word chars (\w)
                           or two non-word chars (\W)
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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use YAPE::Regex::Explain;
print YAPE::Regex::Explain->new("\\B")->explain;
__END__
The regular expression:

(?-imsx:\B)

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  \B                       the boundary between two word chars (\w)
                           or two non-word chars (\W)
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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use re 'debug';
$x = "A\\B";
$y = "Here is A\\B";
print $y =~ /$x/ ? "y" : "n";
__END__
Compiling REx `A\B'
size 4 Got 36 bytes for offset annotations.
first at 1
   1: EXACT <A>(3)
   3: NBOUND(4)
   4: END(0)
anchored "A" at 0 (checking anchored) minlen 1
Offsets: [4]
        1[1] 0[0] 2[2] 4[0]
Guessing start of match, REx "A\B" against "Here is A\B"...
Found anchored substr "A" at offset 8...
Starting position does not contradict /^/m...
Guessed: match at offset 8
Matching REx "A\B" against "A\B"
  Setting an EVAL scope, savestack=3
   8 <Here is > <A\B>     |  1:  EXACT <A>
   9 <Here is A> <\B>     |  3:  NBOUND
                            failed...
Match failed
nFreeing REx: `"A\\B"'
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use re 'debug';
$x = "\\B";
$y = "Here is \\B";
print $y =~ /$x/ ? "y" : "n";
__END__
Compiling REx `\B'
size 2 Got 20 bytes for offset annotations.
first at 1
   1: NBOUND(2)
   2: END(0)
stclass "NBOUND" minlen 0
Offsets: [2]
        1[2] 3[0]
Matching REx "\B" against "Here is \B"
Matching stclass "NBOUND" against "Here is \B"
  Setting an EVAL scope, savestack=3
   1 <H> <ere is \B>      |  1:  NBOUND
   1 <H> <ere is \B>      |  2:  END
Match successful!
yFreeing REx: `"\\B"'
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