Not exactly, ballistic missiles are also guided, but fly a ballistic trajectory.
The term ballistic missile was originally applied to missiles (like the V-2 and Minuteman-I) which were injected into a trajectory by controlling thrust cut-off and flight path angle. After thrust cut-off they flew ballistically. In missile parlance, the portion of the trajectory from thrust cut off to reentry is called the ballistic portion. In tracking radars, recognition of the thrust cut-off is important because the tracking filters use a different propagation model and process noise after thrust cut off. When thrust stops, the missile is said to "go ballistic", and that is the sense in which I was familiar with it for many years. Sometime around 1986, I remember waiting to enter a conference room behind two TRW software engineers who were discussing having told a particularly hot-tempered manager about a five-million dollar overrun. "It was about this time that Ray went ballistic." That was the first time I had heard the expression "go ballistic" used in this manner, although it soon passed into the vernacular.