The York Rite is an appendant body is made up of three different basic groups: Royal Arch Masons, Cryptic Rite Masons, and Knights Templar. The York Rite, which expanded greatly after the American Civil War developed a more military-style while maintaining (more or less) the type of meetings and degrees seen in Blue Lodge.
The York Rite offers Orders - not just degrees - in the Commandery, and the Knights Templar (Order of the Temple) is the only Order between the two appendant bodies that specifically requires candidates to swear to defend the Christian religion.
Additionally, the York Rite is the only body in the United States that confers the Mark Master degree (in other parts of the world - especially in England - they have entire Mark Master Lodges). Why is this important? When the Antients and the Moderns buried the hatchet it was agreed that Freemasonry would "consist of only three degrees and the Mark Master degree." Which, to those of us who can count, means the Freemasonry is actually made up of four degrees; the first three are conferred in a Blue Lodge, while the fourth (which is a pretty great degree) is conferred in a Mark Master (outside the U.S.) or Royal Arch Lodge.
The Scottish Rite is an appendant body that confers an additional 29 degrees (the 4th through the 32nd) although no degree is higher than the Third Degree, which is conferred in Blue Lodge. The Supreme Council (the overall governing body of the Scottish Rite), can award the 33rd degree to members who have performed outstanding service to the Scottish Rite.
The degrees and meeting style of the Scottish Rite differs greatly from the Blue Lodge; degrees are theatrical affairs usually presented on stages with actors and lighting and even music while candidates sit in the audience and watch the play.
The York Rite offers a more familiar Blue Lodge setting, with the Commandery leaning more towards a military bearing (with medals and uniforms and pomp and circumstance) while the Scottish Rite styles itself more as an "educational" body.