Finally, using readdir still gives me the file in ASCIIbetical order

use warnings;
use strict;

opendir my $d, "."; 
print "$_ \n" for readdir $d;
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Result

.
..
1185398.pl
1188996.pl
1153280.serconf
proj1.txt
zipstest
uri.pl
1189013.pl
hash.pm
days.pl
1185438.pl
1189178.pl
hosts.pl
1189178a.pl
1185708.pl
quake_pp.txt
1186032.pl
dumper.txt
1186308.pl
1189211.pl
1186323.pl
1189235.pl
1186469.pl
lookup.pl
1186032-b.pl
1189346.pl
poj.pl
1189381.pl
sqlite-tables.pl
wmi-dbi.pl
1186518.pl
1189436.pl
... omitted for brevity
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it gives you the relative path

readdir also gives you the relative path, relative to the directory you open

So the question is really: how does the file system returns the entries for a given directory?

Yes that is true. Some filesystems use a btree like structure, some filesystems place a new file into the next unused slot in the directory block, where a slot that had contained a deleted file is as eligible before the last block, some filesystems use the next slot that has room to contain the long file name. What order does the DIR command arrange files if no sort order is specified? About the order that readdir() returns entries in

I prefer readdir because it doesnt do things "behind the scenes" such as skip files that begin with a dot. The expression glob(".* *") matches all files in the current working directory.