Master Chief or 117 also known as John-117 (Note the normal name) was part of the Spartan-II program and is a second generation spartan. These were taken to a planet and trained from a very young age.
The third generation of Spartans can be seen throughout the Halo Reach campaign. (all of noble team are Spartan-III) these were also taken from a young age usually orphans from the colonies invaded by the Covenant.
The newest generation of Spartans was the Spartan-IV, this is where the main difference takes place these are voluntary UNSC personnel given a MJOLNIR GEN2 armour suit. (Previous iterations had GEN1 suits)
To surmise, they look so different because they wear a different armour variation to previous generations.
Augmentations for Spartan-IV
Carbide Ceramic Ossification - Advanced material grafting onto skeletal structures to make bones virtually unbreakable.
Muscular Enhancement Lining - Compound applied to the exterior surface of all muscles, allowing them work harder without tearing the Spartan's skeleton apart.
Pulmonary Polymer Lining - Greatly increases oxygen intake and retention, helps process toxins from the air and allows SPARTANs to breathe certain non-oxygen atmospheres for up to an hour.
Corneal Implants - Boosted perception and massively increased night vision.
Cardiac Implants - Strengthens cardio-vascular tissue and increases maximum heartrate to safely allow massive adrenaline flow without the risk of stroke or heart attack. These implants supposedly are able to allow an unarmored SPARTAN-IV to run at a maximum speed of almost 40 miles (64 km) per hour.
Artificial Pancreas Implant - Allows the SPARTAN's body to extract the maximum amount of nutrients and carbohydrates from food with minimal waste.
Artificial Platelet Injections - Enhances the body's ability to slow bleeding and clot wounds.
Source: Halo Wikia - Spartan IV Augmentation Program
The only explanation I can think of is that the Augmentation process becomes improved over time and so they are able to insert the Corneal Implants without affecting the eye colour of the patient.
It is also possible that the spartans you saw just happened to have blue eyes and the corneal implants simply increased the brightness of the colour.
As a comparison to previous generations the Spartan-IIIs used a drug to achieve similar affects to the corneal implants of the Spartan-IVs although they did not gain night vision.
Fun Fact: There actually was no Spartan-I the precursor to the Spartan-II was the Orion Project which also featured augmented super soldiers but they were too costly and fell short of expectations.