Abarim Publications' online Biblical Hebrew Dictionary
It's not clear whether the forms ארז ('rz) and תרז (trz) relate to each other in any way (the ת is often a prefix or formative while the א may drop out in some constructions) but both refer to trees:
The root ארז ('rz) isn't used in the Bible, but it appears to be cognate with an Arabic verb that means to be firm (or to withdraw, curiously enough). In Biblical Hebrew the following derivations are used:
- The masculine noun ארז ('erez), meaning cedar (Psalm 148:9, Isaiah 41:19, Ezekiel 27:5). The colossal Lebanon (that's Phoenician) cedars have been famous since deep antiquity. Mesopotamian mythology tells how Gilgamesh rose to renown after he decapitated a terrible demon who had his haunt in the Cedar Forest, chopped down the biggest cedars and built a fleet of ships and burly city gates. The story seems to tell that what was the refuge of the demon became the refuge of humans (hence perhaps the link between to be firm and to withdraw; "you who dwell in Lebanon, nested in the cedars" — Jeremiah 22:23), and cedars remained the preferred haunt-building material for kings and deities (2 Samuel 5:11, 1 Kings 6:9 to 7:12, Ezra 3:7), which obviously relates to the wisdom tradition as symbol of time-honored certainties on which one may depend and in which one may take refuge (Song of Solomon 1:17, Isaiah 9:10, perhaps also Numbers 24:6). Cedar wood is surprisingly longeval because it contains a natural oil that prevents dry rot and invasion by bugs, which may help to explain its usage in ritual purification (Leviticus 14:4-52, Numbers 19:6).
- The feminine noun ארזה ('arza), meaning cedar-woodwork. This word only occurs in Zephaniah 2:14, where it clearly also denotes the very foundation of a system of wisdom.
- The adjective ארוז ('aruz) of complicated meaning. This adjective is used only once, in Ezekiel 27:24, where it modifies the word for "cords" together with the word for "bound". It's generally translated with "firm," but probably more precise would be "dependable".
Note the somewhat look-alike noun ארן ('oren), which probably also denotes a kind of fir or cedar (Isaiah 44:14 only).
The feminine noun תרזה (tirza) also denotes a kind of tree (scholars guess a cypress) and also occurs only in Isaiah 44:14. It's apparently not known where this word comes from (it might be imported from another language) but if it is Semitic and not a modified version of ארז ('rz), it would derive from a verb תרז (trz), the meaning of which can only be guessed at.