I own a student trombone, and I am looking to purchase a professional one with a trigger.
Does a trigger trombone produce the same sound as a non-triggered trombone of the same manufacturer?
All tenor and bass trombones are pitched the same. The difference between student instruments and professional ones is actually more in the bore size than whether or not the instrument has a trigger (which is typically called an "F attachment").
The F attachment's primary use is to extend the low range of the instrument, and enable technical facility in the middle-low range. For school band use, it typically only becomes necessary for literature played in a good high school band. It is required for modern solo literature and any 2nd or 3rd part orchestral playing. The extra tubing required by the F attachment adds to the weight of the instrument.
Bore size affects the dynamic range of the instrument, the amount of air necessary to play, and timbre in different registers. Smaller instruments aid the high register and are both lighter and require less air. Large bore instruments require a LOT more work, but are capable of a full low register and more volume.
Beginner student instruments are typically .500 bore (small-bore). We call instruments around this size "pea-shooters". F attachments are typically not found on instruments of this size. Professional jazz trombonists will often use instruments around this size (.508, .500) or smaller (<.500), and occasionally dual-bore instruments with large amounts of cylindrical tubing of two different diameters.
Instruments with the F attachment are typically medium-bore (.525) or larger. This size instrument is often used as a "step-up" instrument for beginners, and occasionally for jazz big band players who need the low notes.
Most orchestral players use large-bore instruments (.547, usually) with an F attachment. Some principal players will opt for an instrument without the F attachment because it is lighter, avoids the disruption in airflow caused by the trigger assembly, and they don't require the notes in the low range that require it.
Bass trombones are even larger (>.562) than large-bore tenor trombones, and typically (but not always!) have two triggers of varying tunings (usually F and G, or F and D if they are dependent).
Small- and medium-bore instruments typically accept a small-shank mouthpiece, and large-bore and bass trombones require a large shank mouthpiece.
A conservatory student will almost always require a large bore tenor trombone with F attachment. This instrument is also a good choice for an advanced high school student.
The trigger will slightly affect the tone and free-blowing characteristic of the instrument. If it didnt, ask yourself why manufacturers make such a fuss over their particular rotary valve design, and the "wrap" of the extra tubing! If there was no issue to solve, why are they solving it?
The trigger will give you a few extra notes. It will facilitate agility in the low register. It will not turn you into a bass trombone. It's useful, but not THAT useful. You'll notice that the first trombone player in both symphony and jazz often DOESN'T use a trigger instrument.
While the trigger is not exceptionally helpful, adds weight, and requires you to use more air, it exceptionally develops young trombone player's embouchure. Since these new trombone players have already learned to use the mass amounts of air that us professionals have,it creates new opportunities and opens career options earlier. IT HELPS!
All the F attachment on a trombone does is allows you to reach lower notes and play alternate positions on some notes. (i.e Middle C can be played in 1st position with the trigger instead of 3rd.) The F attachment will help you clear up your low F and E, as it can sound thick and muddy with a normal tenor.
So yes, the trombone will sound 99% the same.