Elements and compounds are different in many ways and for many reasons. I shall explore three ways in which they are different. But in order to understand this you must first understand the nature of an atom. For those of you who aren't obsessed with atoms here is a simple and generally accurate definition, "An atom is the smallest part of an element that can exist while still behaving like that element. So that is to say that an atom of gold will act like a block of gold i.e. they will have same density, etc. Also it is necessary to know that atoms are comprised of electrons, protons and neutrons.
Well now that, that is cleared up I can tell you that an element is made up out of atoms, but a compound consists of molecules (groupings of atoms). This means if one tries to split molecules up into something simpler they would get atoms of elements and the compound would therefore be gone. So therefore we can deduce that a molecule will be made up of elements. This can cause huge differences as when you mix atoms up what you get may be completely different from what you started out with. For example Hydrogen and oxygen are both gases and they combine to make water, a liquid.
Another way in which elements and compounds differ is their chemical stability. Compounds are generally more stable as elements bond in order to achieve stability. The alkali metals are amongst the most reactive substances known. There are six and all react vigorously in water (four will always catch fire and another is likely to). In fact they are so reactive they can't be kept out in the open as in the air they react to destroy themselves so they must be transported and stored in oil. But if you bond an atom of Potassium with a halogen like Chlorine you get a stable compound known as Potassium Chloride.
Another way in which they are unlike is the compounds' ability to enter a fourth state of matter. Although the debate rages about whether plasma is a state of matter or not it is being accepted more widely everyday. The reason for this property exclusive to compounds is due to the fact that a plasma is an ionised gas. An ionised compound is one where elements "swap" electrons if you will resulting in the creation of charged atoms known as, ions. This is because electrons have a negative charge. An element cannot do this as it has no other types of atoms within itself to transfer electrons with.