I saw a video of a jet "drifting" from the air. I don't know if it was the quality of the video or my lack of knowledge with maneuvers but it didn't really do much but just fly over but apparently from the comments they were talking about how it was possible for a jet to "drift" from the sky.
That depends a bit on how you define drifting. I don't think that the definition of motorsport drifting can be applied to a (flying) aircraft. However if you relax the exact definition a bit, you could say that drifting is roughly that your vehicle points (severly) in a different direction then the direction it is travelling. Therefore the vector in which the aircraft points, is (markably) different from its speed vector.l
If you accept this definition, then the answer is: All the time.
A key concept for an aircraft is that of the Angle of attack, which is defined to be the angle between the incoming airflow and the center line of the aircraft. You can see it clearly in this picture (taken from here): The direction the aircraft travels to is marked by the "Velocity" arrow. The velocity arrow corresponds to the airflow direction. The pitch attitude is the angle between the horizon and the centerline of the aircraft. The angle between these two lines is the Angle of attack, or in other words, the angle of the incoming airflow as seen by the aircraft.
The Angle of attack is the prime contributer to how much lift an aircraft produces. The larger the angle of attack, the more lift it generates (up to approximately 15° at which stall sets in).
Therefore (a bit simplified), because all aircraft require a non-zero angle of attack to fly, they all "drift" through the skies (*1). You actually see that in the video you linked. Because the aircraft turns, it requires more lift (in order to go around the corner), hence more angle of attack which is exactly what you see in the video. Some fighter jets take this to the absolute extreme, by performing maneuvers with very large angle of attacks, for example the cobra maneuver (*2).
(*1) There is a small exception, because some aircraft are designed such that in cruise flight, they fly at a 0° angle of attack, but in this sense that is a sidenote.)
(*2) Perhaps as an additional sidenote: the cobra maneuver is enabled by thrust vector control, a technique with which aerodynamic control losses all meaning for these aircrafts.
Based on the appearance of a "drift" in the automotive world, yes.
There's a long complex answer that suggest this is happening all the time, based on a (IMO) sketchy definition of "drift" -- but if you apply that definition only in the horizontal plane, then yes, many aircraft can "drift".
Correctly, in aviation this is called a "skid" and is considered a hazardous maneuver -- for most aircraft it requires crossed controls (i.e. right rudder offset by left aileron to counter roll coupling due to dihedral) but highly maneuverable aircraft, like many warplanes, have little or no roll coupling to rudder input. With these, especially at relatively low speed, a large rudder input will result in the aircraft's nose deflecting and remaining deflected for some time before body lift on the fuselage and fin strake(s) (if present) changes the velocity vector to match the new pointing.
That said, with a lot of altitude cushion (to recover from the unpleasantness that can come from a nose-down crossed control situation like a skid) even a Cessna 152 can make a skidding turn with wings level.