What was the difference between "ye" and "thy"?

Either you remember incorrectly what your professor told you, or he misinformed you.

To take your second question first: ye was the nominative case of the second person plural pronoun (used as a subject, i.e., “ye are” = ‘you are’), while your is the possessive determiner corresponding to the same pronoun (“your house”). The oblique case form was you (“I see you”) The two have never had the same function.

Thou was the corresponding singular nominative, with the oblique case form being thee, and the possessive determiner thy (or thine before a vowel).

As for your first question: the above-mentioned ye was never pronounced [ðiː]; it was [ɣeː], then [jeː], and finally [jiː] in various stages of English. There was thus never any possible similarity between the singular and plural pronouns or their corresponding determiners.

On the other hand, ye was also for a few hundred years semi-randomly used to represent the definite article, which was previously written as þe. The glyph þ (thorn) was used for the sound [θ], and as early as the early 14th century, it had started to be replaced by the digraph ‹th›, as in Modern English. However, in cases where it continued to be used, it lost its ascender, ending up looking first like the older wynn, ƿ (which had almost entirely fallen out of use after around 1300), and later on like a cursive y. That is why the word ‘the’ was for a long time alternatively written as either ‹þe›, ‹ƿe›, or ‹ye›.

The latter of these forms is the only one that’s had any currency for the past couple of centuries, and it is the origin of names like Ye Olde Shoppe. In this case, ye really is supposed to be pronounced the same as ‘the’—though not the same as ‘thee’.

Ye:

(pron.) Old English ge, nominative plural of 2nd person pronoun þu (see thou); cognate with Old Frisian ji, Old Saxon gi, Middle Dutch ghi, Dutch gij. Cognate with Lithuanian jus, Sanskrit yuyam, Avestan yuzem, Greek hymeis. Altered, by influence of we, from an earlier form that was similar to Gothic jus "you (plural)" (see you). The -r- in Old Norse er, German ihr probably is likewise from influence of their respective 1st person plural pronouns (Old Norse ver, German wir).

http://www.etymonline.com/index.php?allowed_in_frame=0&search=ye&searchmode=none

Pronunciation: thee (ðiː) and ye (ði); spelling pron. yi)

The word ye2, as in Ye Olde Booke Shoppe, is simply an archaic spelling of the definite article the. The use of the letter Y was a printer's adaptation of the thorn, þ, the character in the Old English alphabet representing the th- sounds (th) and (th̸) in Modern English; Y was the closest symbol in the Roman alphabet. Originally, the form would have been rendered as or ye.

Thy:

[(pron.) possessive pronoun of 2nd person singular, late 12c., reduced form of þin (see thine), until 15c. used only before consonants except -h-. Compare my/mine, a/an.

http://www.etymonline.com/index.php?term=thy&allowed_in_frame=0

Ye and thee have the same meaning: thou 1 [thou] pronoun, sing., nom. thou; possessive thy or thine; objective thee; pl., nom. you or ye; possessive your or yours; objective you or ye.