A hassock is typically smaller than an ottoman and is almost always round. An ottoman is typically larger and comes in many different shapes. Ottomans can also be used for coffee tables and typically have storage space under the cushion.
Hassocks and ottomans both fall under the category of footstools, though they each are slightly different. Hassocks often are completely covered in fabric, while an ottoman often has legs that can be seen below the fabric. Hassocks can also be knelt on or reclined against because they are often very low to the ground. An ottoman is almost always used to prop up someone's feet because they are taller and larger than a hassock.