They are completely different words. They also illustrate the terrible, horrible, infamous English letter combination "-ough," which is literally pronounced a dozen different ways in a dozen different words. (You just have to learn the pronunciation of every word with "-ough.")
"Through" is pronounced "thru." It means to go into something and then come out in a different place. A train goes through a tunnel. Daylight comes through a window. "I read through the proposal" means I read all of it, beginning at the beginning and continuing through to the end. Figuratively I went in at the beginning and came out at the end.
"Though" is pronounced "tho." It is almost interchangeable with "although." It means "despite," or "but," or "however." "I'm going to walk in the park though there's a chance of rain, because I need the exercise." "Though it is more expensive, it will last longer."
Though it is informal, and you should not use it in normal writing, you may see "through" spelled "thru." This is often done to save space on road signs. In fact, there is a road whose official name is the "New York State Thruway." Similarly, you may see "though" spelled as "tho,"--but usually there will be an apostrophe after the "o" to show that it is an abbreviation. In a famous poem by Tennyson, the speaker, Ulysses, says:
Tho' much is taken, much abides; and tho'
We are not now that strength which in old days
Moved earth and heaven, that which we are, we are...