It’s important to distinguish between abstract concepts in biology, and actual physical things. DNA is deoxyribonucleic acid, a real molecule which can be viewed using an electron microscope, and which (were you very, very, very small) you could poke.
A gene, on the other hand, is just a location, called a locus (locus means location, all hail Latin!) on a specific strand of DNA, which contains the encoded information used to make a certain polypeptide which has a specific role in the development and function of an organism. This code is determined by the sequence of bases (A, T, C and G) at that location.
Think of a DNA strand like a bus garage. All buses look the same, they work the same (just like every adenine base is identical to the next adenine, and every thymine is just like the other thymine), yet every bus has a different number on it. This number is the “gene” – it is just a marker which determines where the bus will end up going once it’s left the bus garage.
What a terrible…