Actually, there are four classical elements, no description (as far as I know) can describe their characteristics perfectly, but I think that this will do: earth (solid), water (liquid), air/wind (gas), and fire (plasma) whereas lightning is a branch of fire, like ice is a branch of water, sand and metal are branches of earth etc.
Also, an element is "the most basic rudimentary piece of", and etymologically, the word comes from the Latin "elementum" (“a first principle, element, rudiment”). In this sense, since snow is shavings of ice which is the solid form of water, magma is heated/molten earth, dust is pieces of earth in the wind, lightning is a higher level of fire or lightning is super-heated fire etc., they are neither "the most basic rudimentary piece of "nor “a first principle, rudiment” therefore cannot and should not be considered "elements".
Therefore, considering this and the historical Greek philosophies which this is based upon, I don't think that we should take "Naruto" as an "Element Handbook"/"Element Bible/Gospel".
Now, having typed that, even in the "Naruto" Universe, Yamato admits that there is no such thing as "Wood Style" nor is there any such thing as the "Wood Element" as it depends upon Earth and Water; they call it "Style"/"Element" for convenience and simplicity, not for accurate categorization.
Yamato - "I can only use Earth and Water natures. You see, technically, there is no Wood Nature." Kakashi - "You use the two simultaneously."
Naruto Book 35. Page 124 OR Naruto Chapter 316: Let the Training Begin!!. (counting the title page) Page 5
Now then, regarding the issue of fire and "plasma"...
"The big difference between regular gas and plasma is that in a plasma a fair fraction of the atoms are ionized. That is, the gas is so hot, and the atoms are slamming around so hard, that some of the electrons are given enough energy to (temporarily) escape their host atoms. The most important effect of this is that a plasma gains some electrical properties that a non-ionized gas doesn’t have; it becomes conductive and it responds to electrical and magnetic fields. In fact, this is a great test for whether or not something is a plasma."
"an ionized gas consisting of positive ions and free electrons in proportions resulting in more or less no overall electric charge, typically at low pressures (as in the upper atmosphere and in fluorescent lamps) or at very high temperatures (as in stars and nuclear fusion reactors)."
Although it may a weak example when compared to say lightning, stars, space storms etc., fire is consistent with the generally accepted chemistry and physics defection of "plasma" (visible ionized gas).