What's the difference between these, and what are their proper uses and meanings? In a historical and modern sense.
I began to wonder about this while researching biblical texts, but this question isn't necessarily in that context.
As an approximation, they're equivalent. For example, an online copy of Merriam-Webster defines sorcerer as
a person who practices sorcery : wizard
and wizard as
(1) archaic : a wise man : sage ; (2) : one skilled in magic : sorcerer
The female equivalent of a sorcerer is a sorceress; very roughly, the female equivalent of a wizard or warlock is a witch, although in figurative modern usage "witch" has strong negative connotations (an overbearing or unpleasant personality, physical ugliness) while "wizard" only has positive ones. An "enchantress" could be a female magic-user more likely to be physically attractive than a witch; but could also be simply a beguiling woman who relies on her physical beauty to gain unfair advantage.
Since you mention the Bible, the words "witch", "witchcraft" and "wizard" seem to mostly be used in the (King James) Old Testament, while the word "sorcerer" seems to only be used in the New Testament. I suspect that that's because of separate translations from Hebrew and Greek; in the Bible, they mean the same thing.
(I'd like to add information about the roots of all these words, and the Hebrew and Greek terms, but don't have my reference-materials handy; I may edit for that later.)