The code below is probably inelegant and perhaps even wrongheaded
but I'm posting, in part, TIMTOWTDI; in part, to illustrate some of the well-taken issues with the likes of AAA29 vs AAA30 (above), and in part, because even though this is NOT a solution, $work calls:

#!usr/bin/perl 
use strict;
use warnings;
 
use vars qw (@fields $field $seen);

while (<DATA>) {
   chomp $_;
   push @fields, $_;
}

for $field(@fields) {
   $seen = $field;
   our $base_seen = substr($seen, 0, -1);   # all but last char of $se
+en
   our $root = chop($seen);                 # get last char of $seen  
+ 
   test1($root, $base_seen);
}

#####subs

sub test1 {              # Excluding the last char, test whether the f
+ields match 

   for $field(@fields) {
      our $base_field = substr($field, 0, -1); # all but last char of 
+$field
      
      if ($main::base_seen eq $base_field) {
         test2($main::root, $main::base_seen, $field);
      }
   }
}

sub test2 {             # bases matched, now test last char for a matc
+h +/- 1

   my $root = shift(@_);
   my $t1 = (shift(@_) . $root);
   my $test1 = shift(@_);
   
   if ( $t1 eq $test1 ) {
      # Returning, t1 is identical to test1 (haven't figured out how t
+o skip this comparison entirely)
      return;
   }
   else {

      # print "\nIn else of test2, ready to cmp: $t1, $test1\n";
      my $rev_last_t1 = reverse($t1);                 # reverse, for e
+ase of m//
      my $rev_last_test1 = reverse($test1);

      #test "last" char which is now the initial char in $rev_last_t1 
+via reverse
      my $last_rlt1 = ord($rev_last_t1 =~ /(.)/);      # numify alphas
+ for +/- below
      my $last_test1 = ord($rev_last_test1 =~ /(.)/);

      if ( $last_rlt1 == ( ($last_test1++) || ($last_test1--) ) ) {
         print "same base and adjacent terminal chars: $t1;$test1\n";
      }
   }
}

# end
# one value added to OP's data:
__DATA__
AAA30
BBC5
SHT12H
DAL33B
BBC49
AAA31
DAL33A
BBC6
SHT12G
BBC50
AAA37
AAA29
[download]

OUTPUT:

same base and adjacent terminal chars: AAA30;AAA31
same base and adjacent terminal chars: AAA30;AAA37  # False positive
same base and adjacent terminal chars: BBC5;BBC6
same base and adjacent terminal chars: SHT12H;SHT12G
same base and adjacent terminal chars: DAL33B;DAL33A
same base and adjacent terminal chars: AAA31;AAA30
same base and adjacent terminal chars: AAA31;AAA37  # False positive
same base and adjacent terminal chars: DAL33A;DAL33B
same base and adjacent terminal chars: BBC6;BBC5
same base and adjacent terminal chars: SHT12G;SHT12H
same base and adjacent terminal chars: AAA37;AAA30  # False positive
same base and adjacent terminal chars: AAA37;AAA31  # False positive
[download]

NOTE1: Fails on AAA29 vs AAA30 and on BBC49 vs BBC50 for (the intended?) reading of OP's definition; if OP had specified "digit" instead of "number" this would not be a failure, but, as is, makes the problem challenging
NOTE2: Fails on AAA37 vs (AAA30 or AAA31) by any reading; this is a glitch in the code /me offers above.
NOTE3: Use any one of several mechanisms, including hashes, to eliminate dupes such as "AAA30;AAA31" and "AAA31;AAA30")

---

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