It's a question of resource availability. Japan had less natural sources of iron and other suitable metals, meaning that what they had was used to make weapons. It's a contributing reason that swords were so tied to nobility in Japan: they were incredibly expensive and precious.

Because of this Japanese armour was made from other materials like wood, leather, cloth and lacquer. These materials are not as malleable as metals, but beyond that there wouldn't have been as much need for tight, gapless armour. Europe warfare developed successively to make use if more and more armour penetration. Longbow volleys, pikes and the like. Knights meeting each other in a melee would grab their stilettos or morningstars rather than their swords. In Japan there wasn't such an arms race to penetrate or bash armour, so in a melee situation something to stop a sword slash was sufficient. If your opponent had a spear they'd be able to get through your armour regardless since metal armour was simply out of the question.

This is of course a wide generalization of an entire culture and their long history, and things varied in different eras, but this is the overall general difference.

They were lightly armoured underneath, such as shin guards, greaves, and sleeves. These adapted as time progressed and fighting style changed, but the actual type of component remained in use throughout. These pieces would generally fall under lamellar armour, a large number of small metal plates/scales laced together, or scale armour, many small metal plates sewn onto a backing of cloth.

There are also theories surrounding the need for an all-weather type armour, where it could stay comfortable in both the hot summers and cold winters while also maintaining minimal rust during humid periods. Materials and general construction techniques could also come into play, where the ability to craft armours from the poorer quality iron sand of Japan coupled with the need to mass produce armours as more recruits were needed in the Sengoku period could also cause the samurai to favour lighter armour. Another idea is that they had more gaps to provide easier movement and better flexibility when riding and managing a bow.

It's also interesting to note the exact idea these armours were made in respect to. European armour was developed with the increasing need to provide full body protection, which lead to the need to create heavier, full-coverage plate. Weapons then changed as well, with heavy weapons such as maces, war hammers, halberds, morning stars, and the like - these were used due to the fact that the force of the blow from any one of those weapons would be more than sufficient to cause damage and crush the armour, rather than pierce it. In contrast, Japan has little to no evidence of mass use of those weapons, as the armour was lighter.

Sources:

• Arms and Armor of the Samurai - The History of Weaponry in Ancient Japan - Bottomley, I.

• The Samurai - A Military History - Turnbull, S.

Japanese Armor was designed around the use of Missile fire with Bows/Yumi which Samurai used mostly along with Spears/Yari and take such fire back without any serious injuries (Matchlock Fire on the other hand...). It was good in the context it was being used, you couldn't use 15th/16th century European full plate Armour effectively for the role Samurai played on the Battlefield.