The trumpet is a pupular brass instrument. Often it's similar counterparts are mistaken for it. The trumpet has three "valves." These are the keys, or buttons on the top that are used to play the instrument. While larger than the others on this list it is considerably smaller than other brass instruments. It is not likely to be confused with a trombone, mellophone, or marching baritone.
The cornet was once more popular than the trumpet. It's design is very similar. If you have a good ear, the easiest way to tell it apart from the trumpet would me it's more mellow tone. The trumpet is often discribed as bright and loud. The cornet is more mellowed and less abrasive in tone quality. Other distintions would be that the cornet is considerably shorter in length. The bell end of the trumpet does not reach out much further than brass slides(tubing that encircles the main body of the instrument).
The pocket trumpet is a musicians nightmare. Designed to be a trumpet compacted to "pocket size" by winding the tubing around more times than a regular trumpet, the pocket trumpet is much a joke. It is near impossible to get properly tuned. Maintaining good sound quality with this is difficult. However, when that is managed, it sounds exaclty like a regular trumpet. The instrument itself is not exactly pocket sized, but it is about half the length of your standard trumpet. Another identifier is the ungodly amount of tubing spiraling around it. If you have large hands, you may not even be able to hold it properly.
If the bugle is the one without buttons, than the piccolo trumpet is the one with four buttons. That's right, it's the only instrument here with more buttons and less tubes. That's because it's a completely different instrument. It is higher pitched, and melodious. Hearing one of these is nothing short of whimsical.
The bugle varies the most of the instruments here. It is the begining of brass intruments, but is still played as a solo instrument. The lack of valves make it challenging to play. Notes are completely dependent on recognizing a tone and adjusting your lips to change it. The bugle is also small, and appears to be the smallest of these instruments by sheer simplicity. Some are made larger for a flashier presentation, and the sound varies from musician to musican as well as bugle to bugle. It is simply, the one without buttons.