Generally speaking, scale armor consisted of multiple pieces of overlapping metal (the scales) attached to a backing, such as lorica squamata.

Lamellar has individual lames attached directly to one another without any sort of backing. These lames are typically connected with a cord of some sort.

In terms of advantages and disadvantages, well, that's a bit trickier to get into. Keep in mind that you're talking about armor worn for hundreds of years in dozens of cultures made out of many different materials. In addition to iron or steel, bronze, leather, bone, and horn can be used for scale, lamellar, or both, and the resulting protective quality will vary significantly. Lamellar made of equal material will typically be heavier than scale and protect better. This is because there is more overlap of lames than scales in most cases.

However, lamellar is not the perfect armor (although it pains me to say this). Due to the exposed cording, it is possible to "cut apart" lamellar, resulting in the lames coming loose. This is somewhat harder to do with scale as there isn't exposed cord and each scale is (typically) riveted to the backing material.

In terms of why a culture would wear one type of armor and not another, keep in mind knowledge and resources were never universal. People used what they could make or purchase with what they had on hand.