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.
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.