They look the same because they are basically the same. An eGO is a battery type, larger in diameter than a cig-alike, that features both 510 and eGo threads, so it's compatible with a wide range of popular delivery devices. Most of the suffixes (-c, -t) are just branding for various accessory bundles. For example, the -c comes with a cartomizer, while the -t comes with a tank system. Prefixes (Joyetech, Vision, Smoktek) usually are branding for the vendors, who are not necessarily the manufacturers -- all of these devices are made in China and many are made in the same factories, side-by-side. You'll find lots of opinions on this forum about the value/quality/reliability each vendor brings to the party.
The batteries themselves are identical in form and intended function. All of them will work with your Kanger T3s. You want to look at battery capacity (650/900/1100 mah) to see how long the battery will last between charges -- about an hour/100 mah. Other than that, shop for price, customer service and consistent quality.
The big EXCEPTION to the above is the variable voltage feature. An eGo Twist (or a Vision Spinner, Smoktech Winder, KGo VV, and maybe some others I don't know) adds the ability to adjust the voltage sent by your eGo battery to the atomizer in your delivery device. Choosing the resistance in your atomizer (for instance, 1.8 ohms or 2.4 ohms) and pairing it with the right voltage from your battery (usually between 3-5 volts) allows you to tailor the vapor produced by your set-up. Changing the voltage, even in small increments, can make a noticeable difference in the taste, temperature and quantity of vapor you get.
Many vapers are perfectly happy with their non-VV eGo devices, and I'd guess most start there. However, in the never-ending search for a better vape, many consider VV to be a significant upgrade. What you choose will depend on your budget, what you need in terms of battery life, and how eager you are to get "fiddly" with your device.
Generally, I think Joyetech, Vision and Kanger are considered top-line brands in eGo devices. Many would also include Smoktech in that line-up. As you'd expect, "no-name" generics can vary widely in quality, but may be such a good deal that they're worth the risk. If you're shopping for your first eGO, I'd recommend you pick a top brand. And buy two. You always need a backup.