What is the difference between clean price and full price?

Clean price is the quoted price excluding accrued interest. Full price, sometimes called dirty price, is the settlement price including accrued interest.

Use:

Full price = clean price + accrued interest

Example: a semiannual bond pays a 4% annual coupon on par of 1,000, so each coupon is 20. If settlement occurs 45 days into a 180-day coupon period, accrued interest is 20 x 45 / 180 = 5. If the clean price is 99.40 per 100 of par, the full price is 99.40 + 0.50 = 99.90 per 100 of par.

The buyer pays the seller accrued interest because the buyer will receive the next full coupon.