I tried a search to learn the difference but got conflicting results. Are you referring to barrel length and/or angle? I always thought howitzer a strange word but never looked into its origin.
It's all about the angles. It's a little something I picked up when I was reading about Germany's weapon development prior to World War I. A cannon is a direct fire weapon. It is designed to have a very low angle of trajectory to deliver a high velocity round onto the target. Not very effective for entrenchments. The howitzer on the other hand is better suited for indirect fire and with its steeper angle of trajectory can drop rounds into an entrenched position better than a cannon can. Then for the next step in the process we have the mortar which basically is a shorter range weapon that can drop munitions almost straight down on someone's head.