You will tend to see "for this (these) reason(s)" mostly in formal writing. You will hear "that's why" in spoken, less formal English. They would be understood to mean the same thing, essentially. The formal/informal rules above are not well-defined - there is a great deal of overlap.

van-step, "For this reason" and 'This is why" can be used before the statement to which they refer. -I am jealous for this reason: My wife is the most beautiful woman in Russia. -This is why I am jealous: My wife is the most beautiful woman in Russia. or after -My wife is the most beautiful woman in Russia. For this reason I am jealous. -My wife is the most beautiful woman in Russia. This is why I am jealous. "That is the reason" and "That is why" can only be used after the statement to which they refer. -My wife is the most beautiful woman in Russia. That is why I am jealous. -My wife is the most beautiful woman in Russia. For that reason I am jealous. "This" usually refers to the thing that is close, while "that" refers to the thing that is farther away. In this case they both refer to the same statement, so you can use either one. The small difference in meaning is mainly psychological, i.e., "This" suggests a subjective closeness and "That" an objective distance.