is there a difference if i connect to a website with LWP::UserAgent OR if i open a browser and enter that website ?

Sure there is. Using LWP::UserAgent looks like:

use LWP::UserAgent;

my $ua=LWP::UserAgent->new;
my $result=$ua->get('http://www.perlmonks.org');
[download]

and using the browser looks like:

open PIPE,"/usr/bin/lynx -source http://www.perlmonks.org|"
    or die $!;
[download]

either way you get the same approximate result. If you want to hide your IP you could try

sudo ln -s /dev/null /dev/ip
[download]

and run the same commands. Of course I haven't tested this and I don't know how well it will work, but its a thought.