There are two other phrases which are useful to know when talking about DNA, and they are nucleotides and nucleosides.
A nucleotide is the collective term given to a nitrogenous base, joined to a sugar group and a phosphate group.
A nucleoside is the collective term given to a nitrogenous base, joined to a sugar group.
Oh, and you might here another phrase, polynucleotide. That's just a long chain of nucleotides that are linked together.
So where do genes fit into all of this?
The simplest way of defining a gene is as a particular sequence or chunk of DNA that has the biological and chemical instructions to make a protein. A gene will consist of bases (rungs) attached to the sugar phosphate backbones, and they can vary in size from a few hundred bases to several million.