There are a couple of important articulation styles that frequently come into discussion of staccato notes.
I call them "notes with closed ends" versus "notes with open ends." The use of one or the other simply depends on the style of articulation you want to have, and how it should sound. I use both styles frequently.
Obviously, starting and stopping note with the tongue at both the beginning and the end of a note gives it a very crisp attack and release. In a rapid-fire section of multiple staccato notes, and at a high tempo, this is the easiest method, because the end of one note essentially serves as the beginning articulation of the next note. This can sound mechanical if the tempo happens to be slow enough where the listener can perceive the rather "brittle" start and stop of each note, but at a high tempo, these sharp attacks and cutoffs are sound fine, and may be preferred. In fact, at some tempos, there is not time for anything besides a "closed end" articulation.
If the tempo allows, I like to use the tongued attack, combined with the "shaped release" of each note, caused by diminishing the air stream. This provides shape to each note (a bit of a taper). This sounds less mechanical. Of course, some tempos don't allow enough time between notes to accomplish all this.
Remember: a steady air stream in all ranges of a wind instrument is PARAMOUNT, and this is a skill that all young musicians need to master. Frankly, the first method (with closed ends) is what I teach to younger students for staccato, so they learn the concept early that the air does not need to be interrupted (or diminished) when articulating lots of notes. That is a good concept for students to master--both in classical music and jazz.
Diminishing the air at the end of a note is a more subtle technique, and gives a very tasteful shape to a note, and is more advanced. However, I find that a little dangerous to teach to students who have not yet mastered the delivery of
a steady air stream to their instruments.
One other method to think about: At some point, a tempo is just too fast to do anything except the initial attack on each note. There is no time to "cutoff" the end of a note or "release" it with diminished air. At that tempo, there
are just a series of notes with an articulation occurring between each one, and there is no difference between staccato and legato--it just becomes notes with brief articulations between them.
UW School of Music