1st answer: TTL means "Through the Lens" exposure control. In this context, it means TTL
flash exposure control. With TTL, the camera measures the light coming back from the scene, and sets the duration of its flash to make a good exposure.
2nd answer: Your current Canon housing is compatible with the S2000, but not directly compatible with the Ikelite DS-51. (You can add an Ikelite manual controller as a workaround, but that only gives you manual control, not TTL). There is a third option, the Sea&Sea YS-01, which is compatible with your Canon housing and well regarded.
Background: When you add an external flash, somehow the external flash has to know what the camera is thinking, when to start and end the flash for good exposure. There are two ways the camera can communicate with the external flash: optically and electrically. Some external flashes use an optical sensor to watch your camera flash and copy it; others have a flash connector for an electrical cord to the flash. Both methods do the same thing -- tell the external flash when to start and stop.
Inon S2000: The Inon S2000 has only an optical sensor, no electrical cord, so it works by optically sensing your camera's flash. To do that the external flash has to "see" the camera flash, using its optical sensor and special circuitry to determine when to start and stop it's own flash. You can easily connect a fiber optic cable to the front of the Canon or
Ikelite housing to channel the flash output up to the S2000. Just use the Velcro attachment supplied with many fiber optic cables. I don't know why DDN said otherwise, perhaps because Ikelite does not encourage this option.
Ikelite G10 housing: The Ikelite housing also has an electrical connector for Ikelite strobes like the DS51 or DS160. This works well. But the Ikelite housing is crippled, apparently for marketing reasons. It limits you to Ikelite strobes, if you want full electrical TTL function. You can't use another brand of strobe in electrical TTL mode on an Ikelite housing, only
manual mode.
For example, Inon makes the excellent z240 strobe, which has both optical and wired connection to the camera housing. But using the wired connection, Ikelite only lets you use it in manual flash mode, not TTL. However, the z240 can set its own exposure, using EA mode, so this is not a real limitation.
Conclusion: You should pick your flash carefully, because it will outlast your camera. You may spend more on the flash, cord, and handle than on the camera and housing. Cameras go obsolete every 2-3 years, flash does not. So, think carefully about what flash features you want long term. I personally think you'd be happy with the S2000, since it works with both the Canon and Ikelite housings today. If you think you might want an Ikelite DSLR housing in the future, then consider the Ikelite DS-51 with manual controller.