"Tho" is not really correct. It is an informal abbreviation of the word "though." As a learner, always use "though." It is correct, and it is not too formal.
"Tho" is sometimes used to save time or space when writing informal notes.
Old poetry sometimes uses the spelling "tho'," with apostrophe after the "o," to show that it is an abbreviation. Why this is done is a mystery to me, but my guess is that in those days careful speakers may have pronounced "though" differently from "tho." You sometimes see things like this in old books. The writer will spell out "pleez" for "please," or "veg'table" for "vegetable," and it is always puzzling because nowadays "pleez" and "veg'table" (three syllables) are the normal way to say the word, but centuries ago they would have been considered incorrect.