Explanation:Convertible bonds. Are corporate bonds that can be converted by the holder into the common stock of the issuing company.
Callable bonds. Called provision option held by the company to repurchase the bond at specific price. Is also called redeemable bonds, jump up etc. While most callable bonds are coupon bonds.
There are no big differences between the two, convertible bonds are often callable, eg corporate bonds can be convertible/callable or the both.