Not necessarily. In some countries it is illegal to advertise for alcohol at sporting events (I think France is one) so there have been ocassions where a new sponsor is made specifically for an away game there or no sponsor at all.
I'd bet my left bollock that they are fakes.
I know the rules on alcohol, they have been in place for many years and either clubs have plain shirts or some marketing gimmick such as LFC having "Probably..." in place of the sponsor. Furthermore, you can only be sponsored by one organisation. If they use two different brand names on home and away kits then that is allowed but Carslberg have nothing to do with Liverpool 08.
So as I said, it's fake.
You can have a different sponsor for games in European countries with said rules, we had Centre Parks on our shirts a few years ago when we played a UEFA Cup game in France because we couldn't advertise alcohol.
You can have a different sponsor, but it has to be from the same organisation like 1878 said before. Scottish and Newcastle owned Newcastle Brown Ale and Center Parcs at that time.
That Liverpool 08 sponsor is definitely fake. I work down here and there's been no mention of it whatsoever.