The Domination League is a 4 month long league (started about a week ago) which is a softcore league (if your character dies, you lose XP, but you don't lose the character).
The difference between it and Standard League besides the 4 month limit is that domination contains shrines that spawn with mobs surrounding it, gaining it's buff. Tagging the shrine gives the player the buff instead.
The Domination League has a fresh new economy, so the prices so various items are quite different from the Standard League, which has been heavily inflated and altered since it first came out (it's been almost a year).
The Domination League also allows players to complete Challenges, completing all within the 4 month period gets you a reward. Some of the Challenges are specific to the Nemesis League though so it's not completely obtainable through just the Domination League.
You cannot play a Standard League character in the Domination League, but, at the end of the 4 month period, all Domination League characters are moved into the Standard League.