Go Noob here, what's the bracketed data (for ranks/rating) explicitly measuring?

Sorry if this isn’t in the correct category, but I am a tad confused on the ranking system.

I understand that the lower the rank, the better the player is. However, the variables that are displayed on one’s profile are vaguely named.

What exactly are “blitz”, “live” and “correspondence” measuring? Why are these variables (for the “rating” row) negative, while the same variables for the “rank” row in the positive?

Please see here: How i can read the stats in my profile?:

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