I'd say it's relative to what day you're using it although I think uvarvu is mostly correct.
In the opening example, I'd assume next/this Tuesday were interchangable, however if using next I'd be inclined to clarify to avoid confusion. Usually I'd use this Tuesday for the Tuesday coming (19th) and next Tuesday for the one after that (26th), but that only applies if say, you're on the Sunday/Monday before the 19th. Using next on say the Thursday 14th, I'd fall back to assuming you meant Tuesday 19th rather than the 26th.
So to conclude:
This Tuesday is always the Tuesday about to follow.
Next Tuesday is subjective on how far away you are. As a rough (and I mean rough) guide:
Wednesday 13th - Friday 15th = This/Next are interchangable.
Saturday 16th - Monday 18th = Next equals Tuesday 26th.