Ions & elements, which is the correct terminology to use when discussing chemical compounds in Earth Science?
Elements are just one specific type of atom. Magnesium, oxygen, sulfur, etc. These are all elements.
Compounds are several different types of atoms (that is, elements) bonded together. For example, magnesium oxide (MgO), or iron sulfide (FeS).
Ions are charged atoms or compounds (also known as species in some cases). Ions can be monoatomic (consisting of only one atom, or element) or polyatomic (consisting of more than one type of atom). Cations are positively charged (like Ca2+) and anions are negatively charged (like O2-). Polyatomic ions that occur in geological contexts are usually anions, with carbonate (CO32-) and sulfate (SO42-) being two good examples.


All ions are elements (or combination of them). Not all elements are ions. We geologists and geochemists use these terms interchangeably all the time. I think that using ions may be slightly better, particularly in the case of sulfur. Because sulfur in minerals can be either in sulfate or sulfide form, just saying "sulfur" gives little information. The properties of sulfate and sulfide minerals are completely different, so it's actually useful to know.


  Sulfide ions (S2-) bond with a number of positive ions to form the sulfides


Not strictly correct, because the bonding in many sulfide minerals is a combination of covalent and metallic bonding, and it only has a little ionic character. Still, even in cases when the bonding is not ionic (such as in sulfide minerals), we still often talk of them of ions because it's convenient and easy.


  Sulfide minerals consist of metallic elements in chemical combination with elemental sulfur


This statement is not correct. When we speak of "elemental" elements, we mean that they are monoatomic compounds (or minerals). In the case of sulfur, it will be the yellow sulfur mineral. Gold, copper and silver and other example of "elemental" minerals. Once the sulfur is bonded to other metals, it is no longer elemental. It is part of a sulfide mineral.