With Tu B'Shvat coming up, lets look at two Hebrew words for tree: etz עץ and ilan אילן.
I actually discussed the etymology of etz in the comments on my post for lute, in response to the question whether the Hebrew עץ is related to the Aramaic אע (of the same meaning):
Steinberg connects etz to a root עצה meaning "to bind, attach, strengthen", and is related to such other words as עצה / עצם - "to close (the eyes)", עצם - "to be strong, mighty", יעץ - "advise, give counsel", and עצב - "give form, shape".
Klein's etymology for עץ :
"Related to Phoen. עץ (= wood), Aram. אץ (dissimilated from עץ) , Egypt-Aram עק, Ugar 's, Arabic 'idah, Ethiopian 'ed, Akka isu (= tree, wood)."
Klein doesn't mention אע, but perhaps he feels it developed from אץ.
Kutscher, on the other hand, writes that really the Aramaic word should have been עע, but two guttural letters couldn't stay next to each other, and due to dissimilation, the first ע became an א.
Ilan is originally an Aramaic word, only appearing in the Tanach in the Aramaic section of the book of Daniel. Klein writes that it is related to the Hebrew elon אלון - "oak" (as in Alon Shvut). Elon is related to ela אלה - also meaning "oak, terebinth", and Klein connects all of them to the root אול - meaning "to be strong". This is similar to Steinberg's etymology of etz, and it's not surprising - a tree was (and still is) a symbol of strength. From אול we get the animal names ayil איל - "ram" and ayal - "deer". Klein writes that many once derived el אל - "god" from אול, but he does not find the argument convincing.
Kutscher asks the question - "Why don't we call Tu B'Shvat 'Chag LaEtzim' instead of 'Chag LaIlanot' ?" His answer is that in Biblical Hebrew etz meant both "tree" and "wood". But in the times of Mishnaic Hebrew, ilan had entered into Hebrew from Aramaic, and now there was the ability to have two separate terms - etz for wood and ilan for tree.
This distinction can explain why Rashi on Bereshit 18:4 found it necessary to explain tachat haetz תחת העץ as tachat hailan תחת האילן. He was trying to point out that the guests sat under a tree, and not under a wooden roof.
There are of course some exceptions to this "rule" - most notably the blessing "borei pri haetz" בורא פרי העץ.
Modern Hebrew tends to prefer Biblical over Mishnaic Hebrew, and so we generally use the word etz for tree (except when talking about Tu B'Shvat.)