The exact definition of a howitzer has changed in modern times, and is not entirely standardized. One of the initial defining features of a howitzer -- that it was loaded by hand -- became occluded by its battlefield capabilities, and eventually faded into obsolescence.
In the late 1690s and on into the early 1800s, a howitzer was defined by its form, which in turned defined its niche in the battlefield; it was a small piece of mobile battlefield artillery, a modification on the cannon in which the charge and the shell were loaded by hand. As such, the barrel could not exceed the length of the average gunner's arm. This in turn impacted its accuracy over longer distances, and therefore also limited how large a powder charge it was worth loading. A howitzer did not fire as far as a canon, which fired balls with a large charge on a flat trajectory; and it fired further than a mortar, which fired using a smaller charge and a high angle, useful for getting explosive shot lobbed over walls during sieges. The howitzer was between these in length of barrel, in the size of charge, in the distance and height fired, in accuracy, and it additionally could be used to fire either balls or shells, depending on need.
In 1822 Henri-Joseph Paixhans developed advanced fusings that allowed explosive shells to be fired at higher velocity -- and thus flatter trajectories, resulting in greater accuracy -- without prematurely exploding, thus upending naval warfare and spelling the eventual end of wooden warships. Small, accurate, artillery that fired explosive shells turned out to be really quite useful on land as well, and by the mid-1800s it was hard to tell a light cannon from a gun-howitzer -- that is, a "howitzer" with a longer barrel.
This vague in-betweeness remains. With modern military technology the trend is towards longer barrels on all forms of gun, very few cannonballs, and good distance -- and accuracy -- even on high-angle trajectories. Currently the U.S. military defines a howitzer purely on the angle that it can fire at: any artillery piece capable of both high-angle (45° to 90° elevation) and low-angle (0° to 45° elevation) firing is a howitzer, while 'guns' are defined as those pieces being only capable of low-angle fire, and 'mortars' are defined as those being only capable of high-angle fire.