Most people are aware that politics can affect how history is recorded. But every scientific endeavor suffers from such things.  In biology, zoology has gone through the same sort of thing.  When you are dealing with anything subjective (and lots of things in science is subjective) politics come into play.

And few things are more subjective than organism classification.  With that said, zoologists have a basic classiciation system. It's not perfect, but it is accepted and that's what matters.

Lay people tend to mix up the different types of classifications on a regular basis.  So here is a chart of the basic ordering of creatures on Earth:

The basic unit of organism is species.  If creature A and B and reproduce together and produce offspring that can reproduce, then they are the same species. If they can't, they are different species.

Hence, a Poodle and a St. Bernhard are the same species -- they can (unfortunately) reproduce. 

Moving up you have similar animals.  A Lion and a Tiger are both types of cats. But they are different species. They cannot reproduce viable offspring.

Further up you have Families.  Dogs and Cats are actually quite similar.  But they're obviously not very closely related.  But they are in the same basic family of animal.  They are, a lot more similar than say a Cat and a Mouse or a Dog and a cow.  Dogs and Cows are both in the same order.  They're both types of mammals. 

Next up you have classes. Now you're really talking different things.  Mammals and birds are a lot more similar to one another than say Insects.  So Mammals and birds would be part of the same Phylum and Insects would be in their own.

And then finally you have Kingdom.  Animals and Plants for example. There's also fungus, and protistas which should be called "Pretty weird stuff".  And there's even one above this not regularly referenced but if you're really geeky like me you can talk about and that's Domain where you have Bacteria, Archaea, which I've never seen as they live in extreme environments. They were probably amongst the first lifeforms.  We're part of the domain Eukarya incidentally.

That said, once you get outside species, things get more subjective.  For instance, Bacteria, why should they get their own Domain? Couldn't they be argued as a plant? Admittedly, I doubt there are message forums where PhDs sit there and have flame wars over the classification of bacteria.