SSG (Super Saiyan God)
SSJG (Super Saiyan God) is the god form that Goku unlocked in DBS. This happens when a new threat Lord Beerus the God of Destruction enters Earth to find the legend of the Super Saiyan God. He has the power to destroy planets at will. Goku achieves this form through a special ritual where 6 pure-hearted Saiyans hold hands in a circle to install their light (ki) into one person. If done correctly the SSJG form will appear. It's appearance consists of crimson coloured hair - shaped to look like Goku's base form hair - and a slightly thinner phyique compared to his normal size. Instead of a traditional SSJ aura, it is an aura of flames/fire. This form puts the Divine Power of Gods into Goku's body. It is x20000 stronger compared to base form.
SSB (Super Saiyan Blue)
SSJB (Super Saiyan Blue) is a form that Goku has in DBS. It was introduced in his battle against Golden Frieza. Goku achieves this form, along with Vegeta from training with the God of Destruction's servant and master, Whis. It's appearance comes with blue hair, shaped like that of a Super Saiyan. The aura surrounding him has turned blue as well. The form is basically the power of a Super Saiyan mixed in with the Super Saiyan God form. The form is also called Super Saiyan God Super Saiyan (SSGSS). It is x100000 stronger compared to base form.
UI (Ultra Intinct Omen)
UI (Ultra Instinct) is a form unlocked by Goku in Dragon Ball Super. Goku achieves this in the Tournament of Power after accidentally consuming a Spirit Bomb, pushed back by his biggest foe yet, Jiren. The form allows the user to react to any threat without them acknowledging it and gives them the ability to adapt to their surroundings in battle. Goku's way of fighting changes too. He uses this form to fight Jiren in T.O.P (Tournament of Power). The image above shows the supposed mastered version, made by fans. This form comes with bright silver eyes, dark silver hair slightly raised up, a blue aura with white highlights with sparkles that come with godly ki. A quote in the anime says "He's emitting a tremendous amount of heat, but... his energy seems frighteningly calm." This basically means that his aura is like that of Lord Beerus. A Hakaishin, a gentle flame that emits loads of radiation and clings to the body. His strength compared to his base form is unknown.
MUI ( Mastered Ultra Instinct)
MUI (Mastered Ultra instinct) is the latest form, to date, that Goku unlocks in the Tournament Of Power, this form is the complete version of Ultra Instinct. After seeing this form, the Gods of Destruction from each universe stood up to show respect for Goku achieving this form. Others have achieved this form before him, Whis and the rest of the angels. It comes with grey hair and a larger aura compared to the incomplete version. Even the aura is hotter , burning away his clothes when he tapped into it. Theories state that Goku had created a tiny galaxy when he released his energy. The strength compared to base in this form is unknown.