Spartan-II's-Children abducted at the age of 6. Had intense training. Later given augmentations for bones, strength, speed, sight, agility, hearing and reflexes. They had a black body suit, than Mark IV Mjolnir armour, then Mark V Mjolnir armour, then Mark VI Mjolnir armour and a few had Mark VII Mjolnir armour. IMO the best Spartans. Master Chief was one of them. Known as Spartan-117. There was funding for 300 Spartan-II's. It was later reduced to 150 of them. It was reduced once again to 75. Some are still alive. Very disciplined
Spartan III's-Orphans taken and trained by Kurt-051, a Spartan-II, and CPO Mendez, trainer of Spartan-II's. Less extreme augmentations. Used SPI (Semi Powered Infiltration) armour. Some used Mark V armour, such as Noble Team during the fall of reach. (BTW Jorge in Noble Team was a Spartan-II, the other five were Spartan III's). There were more of these spartans but they were "disposable". They were sent on extreme tactical suicide missions and had a 90% chance of death. They weren't as good as the Spartan-II's but were great soldiers. Some are still alive.
Spartan IV's are adults that volunteer to join.They use Mark VII Mjolnir Gen2 armour. They have less severe augmentations and aren't as powerful as Spartan-II'' or Spartan-III's. They aren't as disciplined as the other Spartans. I personally don't like them as much. There are many of them aboard the UNSC Infinity.
Spartan I's are just normal augmented humans. It was a failed project. Sgt. Johnson was one of them. That's why he is resistant to the flood and can't be infected.
Mjolnir Gen 2 armour is any model from Mark VII and onward, I think. The suit that master chief has is the first Gen. It looks different in Halo 4 for two reasons.
1) New artwork
2) Whilst Chief was in Cryo sleep, Cortana used nanobots to slightly modify his armour.
Hope this helped