For guitar, I'm having a hard time trying to understand the difference between chord inversions, open voiced triads and drop 2 chords.. currently I'm trying to study the essential chords in Ted Greene's Chord Chemistry (1971) but the chords are just there without much explanation so I'm lost.
Chord inversion simply refers to which note is in the bass (i.e., the lowest note). We start in root position with the root in the bass: for a C major chord, C is the lowest note. If we imagine a simple C-E-G triad, then we can "invert" the chord by moving the C up an octave, getting E-G-C, with E (the third) in the bass. This is first inversion. We do this again to get G (the fifth) in the bass for 2nd inversion. Seventh chords have a third inversion. It doesn't have to be a block chord like this--any C major chord with the lowest note of E is in first inversion.
Open vs. closed voicing is how far apart the notes are. Closed voicing is like what I described above--the notes are as close together as possible. An example of an open voicing would be C-G-E, with intervals of a fifth and a sixth between the notes.
Drop 2 chords are a type of open voicing commonly used in finger style guitar. Notes are fretted on the 1st, 3rd, and 4th strings, and the 2nd string is "dropped" from the voicing. It leads to very convenient and effective jazz voicings.
I agree with @MattPutnam's answer as far as chord inversions and close/open voicings are concerned, but I'd like to add an explanation of what drop voicings are.
First of all, there are no "drop 2 chords", there are only drop 2 voicings of chords. The concept of drop voicings is often applied to four part chords. A drop voicing is obtained by dropping one note of a close voicing by one octave. In a drop 2 voicing, the second note from the top is dropped by one octave. You also have drop 3 voicings, and drop 2-and-4 voicings. Drop 2 and drop 3 voicings are very common on the guitar because they can be played very easily (unlike most close voicings of four part chords).
As an example, take a Cmaj7 chord. One close voicing is (from low to high) C-E-G-B. You get a drop 2 voicing by dropping the second note from the top (the G) by one octave: G-C-E-B. On the guitar, this voicing is most easily played on four adjacent strings. Either on the top 4 strings:
X X 5 5 5 7
or on the middle four strings:
X 10 10 9 12 X
(of course it can also be played on the lowest four strings, but this is less commonly done).
The drop 3 voicing of the same original close voicing would be E-C-G-B (because the third note from the top is dropped by on octave). Drop 3 voicings on the guitar are usually played on non-adjacent strings. The bass note is either played on the low E or on the A string, and the other notes are played on 3 adjacent strings, either on D-G-B (if the bass note is on the low E string), or on G-B-E (if the bass note is on the A string):
X 7 X 5 8 7
12 X 10 12 12 X