Hearthstone Global Games are weekly team-based competitions comprised as follows: "Each team in the HGG will consist of the top Hearthstone Competitive Point earner from their country and three of their fellow community-voted countrypersons."
Meanwhile, the Hearthstone Inn-vitationals are more of a pick-up competition featuring streamers, tournament victors and "celebrities" who play.
In terms of payout, Hearthstone Championship Tour grand prize will be over $2 million next year while the World Championship has $1 million up for grabs, $250,000 for season championships. Playoffs for seasons will have "at least" $20,000 in prizes.
For the nitty gritty of how each style of tournament will change, head over to the source post.