Abarim Publications' online Biblical Hebrew Dictionary
The two particles כ (ke) and כי (ki) are probably closely akin, with the ubiquitous adverb כה (koh) as their distant cousin. Their shared function is to compare one idea with another. The main difference between the first two is that כ (ke) is an inseparable prefix and כי (ki) is a word.
Also note that as a postfixed particle, the letter ך (k) serves to indicate the second person single: you.
The inseparable prefix כ (ke) expresses a comparison to the noun it is attached to. Most literally it means something like "in the manner of" and mostly ends up being translated as "like" as in: X, like-Y. But often "like" doesn't cut it, and translations speak of: about, according to, and even when or while. This prefix occurs very often in the Bible, but perhaps most prominently in the name Michael, or mi-ke-el; "who [is] like God?". Our particle is part of the following substantives:
- The substantive כמו (kemo) is כ (ke) plus the particle of inquisition מו (mo) and literally means something like "in the manner of the essence of..". It's used in the same way as כ (ke), but mostly in the poetic texts of the Bible and is possibly a bit more deft and theatrical.
- In combination with the relative particle אשר (asher), which generally means who or which, our particle כ (ke) forms the conjunction כאשר (ka'asher), which would meaning something like "according to that which..".
The substantive כי (ki), expresses "a temporal, causal, or objective relationship among clauses expressed or unexpressed" (in the elegant words of HAW Theological Wordbook of the Old Testament). It's used more than 4,000 times in the Old Testament and can most often be translated with "that" or "in that (= because)" or "in that (= when)".
The ubiquitous adverb כה (koh) means thus and occurs in a wide array of phrases, such as 'thus says the Lord' or 'thus you shall say'.