Thee is an object pronoun — the old singular equivalent of "you" when it receives the action: "I give this to thee." Thy is a possessive determiner, the old equivalent of "your", and it must sit in front of a noun: "Thy kingdom come." If a modern rewrite would use "your", the word is thy.
The core difference
These are not interchangeable stylistic variants — they do different grammatical jobs, exactly as you and your do today. Writers reaching for an archaic register often use thee everywhere, which produces sentences like "thee house" that no historical text would contain.
The pronoun set
It is easier to see when you lay the whole set beside its modern equivalent:
- thou = you, as subject — Thou art late.
- thee = you, as object — I saw thee. / with thee
- thy = your, before a noun — thy sword
- thine = yours, standing alone — The victory is thine — and also "your" before a vowel or h: thine eyes, thine own heart
Note that thy and thine divide the work the same way my and mine do, which is a reliable crib: wherever you would say my, say thy; wherever you would say mine, say thine.
The test
Rewrite the sentence in modern English. If it comes out as your, use thy. If it comes out as you and that you is receiving the action or following a preposition, use thee. "Blessed art thou amongst women" gives "you are" — subject, so thou. "Hallowed be thy name" gives "your name" — so thy. "To thee we cry" gives "to you" — so thee.
Where you will actually meet them
Both forms disappeared from ordinary English speech centuries ago and survive today in the King James Bible, the Book of Common Prayer, hymns, Shakespeare, and — still living, not quotation — in traditional dialect in Yorkshire and parts of the north of England. If you are writing pastiche, the risk is not sounding archaic enough; it is sounding archaic in the wrong places.
The mistake to avoid
Thy cannot stand alone. "This book is thy" is wrong; it should be thine. And thee cannot modify a noun: "thee crown" is never correct. If a noun follows immediately, your only options are thy or thine.
One more consequence worth knowing: thy and thee are singular. Addressing a crowd, historical English used ye (subject) and you (object) instead.