The study of insects is called: Entomology.
Most everyone calls any insect that they see a bug, weather it's a beetle or an insect of a spider.
Just to start things off right, spiders are neither bugs, insects or beetles, they are Arthropods -or Arachnids. Now those come later so we aren't gong to cover them to day.
Here's the basic run down.
Insects: Have a Head, a Thorax and a Abdomen. The Insect has two sets of wings. Now you must remember that there is always an exception to every rule - even in science, so later we might come across an insect that has three sets of wings.
Beetles are often identified by the fact that they have a hard outer shell.
So there is a little on insects and bugs for now.