I'll answer your questions with as much info as I can but first I wanna give you a suggestion based on how I got into
pyro.
There is a written prerequisite of having assisted 5 public displays for the Pyrotechnic Operators, and I'm sorry if I'm overestimating here, but I'm going to guess if you need to ask what each license is for you probably haven't done that. The other two licenses don't have a written prerequisite, but I assure you they do not give them out like candy.
In most states (and countries for that matter) you don't need a license to assist with a pyrotechnic event, you just need a licensed operator in charge of the whole thing. Because of this often times you need to show compelling prior experience before you can test for a license. Texas does their licenses in a different way than many places so I don't know for sure if this holds true in your state.
The best thing you can do is contact someone who knows for sure, the
AHJ would be a good choice as they can tell you exactly what they want to see before they'll give you the test. Even better though, if you can get a hold of a special effects company in the area they can tell you what they would want to see before they hire someone, and they will more than likely be able to tell you the same information you would get from the
AHJ. The key to that conversation would be making sure that they know you're looking for information first and a job second (if at all).
Pyro is one of those "
break-in" fields where everyone wants someone with a good amount of experience and no one wants to train someone without it. If you want to do
pyro (especially in Texas) you're probably gonna have to
call around and make some friends in the industry.
Now to your questions:
From reading your attached PDF the Pyrotechnic Operator’s License could more generally be called and outdoor fireworks operators license, the Pyrotechnic Special Effects Operator’s License is for proximate audience (read indoor
pyro), and the Flame
Effect Operator is for anything using flame effects (primarily liquid propane effects). As for which one to get, any you can. The Special Effects Operator followed by the Flame Operator will be the most use in entertainment, but to be entirely honest the licenses are $45 bucks each the first time, and $25 each to renew. If it was me I'd carry all three.
The Texas licence is one of the hardest to get in the nation, because of this if you do get licensed it'll go a long way with AHJs in other states. In places where they are really picky about
pyro licencing (Illinois, Texas, and New York for instance) it's pretty common for a touring company to hire a local "
pyro shooter" so that you have someone from the area with a licence.
What having a
pyro licence means is hard to define. This is because it doesn't matter what you, the state, or your company thinks the licence is good for, it matters what the
AHJ thinks it means. In Florida you are licensed by the city not the state, so in theory your license is only good within those city limits, but practically applied most AHJs nation wide just want to see that you have a license.
Apply this internationally and it gets even more complex, In Quebec you have to have someone on the show with a Quebec
pyro licence (which is different than the Canadian national licence). They are a really big pain about getting one person there with that license, but once you hire one person, they will give temporary sponsored guest licenses to almost anyone with a licence from anywhere.
In a lot of European countries they don't even ask about a license, they want to know about how the show is designed, how many shows this design has done, any problems you've had, and what past experience you have that makes you a qualified operator.
So basically a
pyro license is a great thing to have on your resume, but if you're actually looking to do
pyro experience is worth way more.