Ok, so you are kind of wrong. Not everybody has elemental chakra. Lee for instance does not. Also what you explained is a combination element jutsu. And cant be used at the same time unless you can channel two chakra natures at once. And those who can utilize both elements at once can have access to a KG. KG is the birth of a new element by combining two elements, and you can take it even further. A KT (Kekkai Totou) is 3 elements. Only known users to have a KT is Oonoki and Mu, who posses dust release. Normal ELEMENTAL KG (Excluding dojutsu users) are Scorch (Fire and Wind) Steel (Fire and Earth) Storm (Water & Lightning) etc etc.
Im sure you know about the elements irl. But In naruto context, Fire is the element, specially to the Uchiha as each uchiha posses the fire chakra nature. Fire can be used to burn, and explode.
Water represents life, even in naruto. Known water uses are tobirama, mei, yagura. Etc. Water techniques arent normally lethal, but very flexible and can be used in multiples cases (Vapor in the air, water source, from the mouth, sweat from the body, rain. Etc) Also its very flexible and can change nature, such as making it sticky.
Earth (which is my favorite element) Represents balance. Due to its offensive and defensive nature at the same time. Known users are kakashi, Kagatsuchi, Oonoki . Etc. Earth though being really good for defense, being the sturdyness and the only one with a true solid foundation. But its the 2nd most destructive element (first being lightning) If you know how to use earth right (Which im going to teach you) You can not only use most your earth jutsus to defend, but go on the offensive at the same time.
Wind represents peace IMO. Wind users are Naruto, Sora (If you seen the fillers), Asuma, etc. Wind is normally used as a slicing or breeze type jutsu, and can be used as both even.
Lightning represents destruction. Lightning is the most destructive element, not only cause its abrasive nature, but it also destroy earth which is the 2nd strongest element. Lightning users consist of Kakashi, Sasuke, Darui, Raikage, etc. Lightning in naruto is not only used for offensive nature but to even augment the users strength and defense (3rd raikage) and speed (4th raikage). You can use this from thunder clouds, regular clouds, your body. Etc
Im missing alot, but this is the BASIS of what those elements mean .
Any questions? Also what is your favorite element