To build on tobyink's post, remember that it's easy to try things out:

Updated with the Inf test case suggested by syphilis.

use warnings;
use strict;

my @testcases = ( [1,-1], [1,0], [1,1], [1,2], [1,3],
    [9**9999,9**9999] );
for my $sub (qw/ doit1 doit2 doit3 doit4 /) {
    print "-----\n";
    for my $testcase (@testcases) {
        print "$sub($testcase->[0], $testcase->[1]):\n";
        # for this test only, not recommended otherwise:
        no strict 'refs';  &{$sub}(@$testcase);
    }
}

sub doit1 {
    my ($x,$y) = @_;
    if ($x==$y) {
        print "\tThey are equal, do something\n";
    }
    if (abs($y-$x)<=1) {
        print "\tThey are within +/- 1, do something else\n";
    }
}

sub doit2 {
    my ($x,$y) = @_;
    if ($x==$y) {
        print "\tThey are equal, do something\n";
    }
    elsif (abs($y-$x)<=1) {
        print "\tThey are within +/- 1, do something else\n";
    }
}

sub doit3 {
    my ($x,$y) = @_;
    if (abs($y-$x)<=1) {
        print "\tThey are within +/- 1, do something else\n";
    }
    elsif ($x==$y) {
        print "\tThey are equal, do something\n";
    }
}

sub doit4 {
    my ($x,$y) = @_;
    if (abs($y-$x)<=1) {
        if ($x==$y) {
            print "\tThey are equal, do something\n";
        }
        print "\tThey are within +/- 1, do something else\n";
    }
}

__END__
-----
doit1(1, -1):
doit1(1, 0):
    They are within +/- 1, do something else
doit1(1, 1):
    They are equal, do something
    They are within +/- 1, do something else
doit1(1, 2):
    They are within +/- 1, do something else
doit1(1, 3):
doit1(Inf, Inf):
    They are equal, do something
-----
doit2(1, -1):
doit2(1, 0):
    They are within +/- 1, do something else
doit2(1, 1):
    They are equal, do something
doit2(1, 2):
    They are within +/- 1, do something else
doit2(1, 3):
doit2(Inf, Inf):
    They are equal, do something
-----
doit3(1, -1):
doit3(1, 0):
    They are within +/- 1, do something else
doit3(1, 1):
    They are within +/- 1, do something else
doit3(1, 2):
    They are within +/- 1, do something else
doit3(1, 3):
doit3(Inf, Inf):
    They are equal, do something
-----
doit4(1, -1):
doit4(1, 0):
    They are within +/- 1, do something else
doit4(1, 1):
    They are equal, do something
    They are within +/- 1, do something else
doit4(1, 2):
    They are within +/- 1, do something else
doit4(1, 3):
doit4(Inf, Inf):
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