How is organic chemistry different from regular chemistry?
Organic chemistry is the study of carbon compounds.
Carbon is special. It is small, having only 6 electrons. Two of them are in the low energy inner cloud, leaving four in the outer cloud where they can form bonds with other atoms. These two things are what make carbon special.
Being small, carbon can easily fit into molecules that would not have room for larger atoms. Being small also means that the electrons are close to the nucleus, so strong bonds can be formed.
Having four outer electrons means that carbon also has four empty slots for electrons from other atoms, since the second electron shell has room for eight electrons. Carbon can form lots of bonds with other atoms, forming long chains, loops, sheets, branching tree-like structures, and many other forms. This versatility is what leads to life. We call carbon chemistry organic because life is based on carbon compounds.
Organic chemistry is the study of carbon compounds whether or not they come from living things. We see carbon compounds in interstellar dust, and inside meteorites, in coal and petroleum, and in the flames as carbon based fuels burn. Organic chemistry is usually thought of as the chemistry of compounds that have a C-H bond (carbon bonded to hydrogen), although there are organic molecules that have no hydrogen, such as Teflon.
The study of chemical reactions in living things is a separate branch of chemistry called biochemistry. Of course the two fields (organic chemistry and biochemistry) are closely related and overlap in many areas. Inorganic chemistry also overlaps with organic chemistry, as many simple carbon compounds such as chalk and carbon dioxide are considered inorganic, even though both are usually made by living things.