The meaning of siege is when you surround a person's castle with your soldiers and conquer it.
source: http://www.dictionary.com/browse/siege
The meaning of ballista is basically a very big crossbow, but instead on holding the ballista it is on a wooden plank or on a tripod or a stand. The ballista also throws spears also known as a bolt during the Middle Ages. A ballista is kinda like a big spear throwing machine. The ballista works by using tension.
source: https://users.ece.cmu.edu/~koopman/ballista/defn.html, http://www.lordsandladies.org/ballista.htm
