You'd first off do well to keep your lighting questions on one thread. You've got another thread running on this same topic over here:
https://forums.saltwaterfish.com/t/349372/lighting-help-me
If you've got people helping you on two different threads, it's only gonna confuse you more. You should pick a thread, put a post in there asking the moderators to close it, and work on the other thread.
Also, you probably should beware that it's against the forum rules for us to tell you where to go online to buy items. Saltwaterfish.com does not permit links to competing web sites or for us to even directly mention them. The rules can be bent... but only a little. So unfortunatley I nor anyone else can give you a direct pointer on where to go.
Okay rules and lectures out of the way... I'll try to explain this a bit for you. I know what it's like to be starting out in this stuff!
One of the things that is probably confusing you is that T6 is a very rare and obsure type of lighting system. There is only one main manufacturer that markets them (that I know of) and this particular manufacturer (Jebo/Odyssea) is really low quality. T5 lamps are the common ones of similar size.
The first thing you need to know is that when dealing with regular fluorescent tubes (straight tubes), the "T" designation refers to the diameter of the tube. The number is the number of 1/8" increments the lamp is in diameter.
1/8 of an inch = 0.125 inches.
Therefore, a T5 lamp is 0.125 * 5 = 0.625 or 5/8 inch. So a T5 lamp is 5/8 of an inch in diameter. Make sense? Hopefully that makes these "T" numbers easier for you to understand.
The most common diameter lamps you find in the aquarium world are T5, T8, and T12. If you apply the above math, you'll find that:
T5 = 5/8 in diameter
T8 = 1" in diameter
T12 = 1.5" in diameter.
For a point of reference, T12 lamps are the ones you commonly see in those 4 foot 2 lamps workshop fluorescent lights.
Now, T5 lamps are nearly always only available in "high output." They are available in several lengths. For the sake of keeping this simple, I'm not going to go any longer than 36".
24" - 18 watt
36" - 39 watt
T8 lamps only come in "normal output" for aquarium use. These are the lamps that you most often see at chain stores like *****, PetSmart, etc. These lamps are for normal aquarium lighting, and lack the intensity required to keep most if not all corals.
15" and 18" - 15 watt
24" - 20 watt
30" - 25 watt
36" - 30 watt
Notice here that there is a 20 watt size. This is where I am wondering what your LFS is telling you. T5 lamps don't come in 20 watt, T8 lamps do. This is why I wonder if they are either mistaken or lying about one of those specs.
What I'd do if I were you is go back to that pet store and look at the tubes. Look at the diameters I listed above and compare it to what is in that light. See if you can figure out for yourself what kind of lamps it has.
Also, shop around online. If you use Google to search for T5 Aquarium Lighting, you should find many useful links. Compare prices. What I said in the other thread applies though... expect to spend $300 - 400 on a decent lighting system for a reef tank. Local prices are almost always much higher than for a similar system online. Anything less than $300 is probably either A) a crappy system or B) an insufficient system.
I hope all this helps. Feel free to follow up wtih more questions. There are lots of smart members here who are more than willing to help!