"Light" refers to API gravity, roughly 37 to 42 degrees for the deliverable grade. "Sweet" means sulphur below 0.42%. Both matter to refiners: heavy, sour crude needs more processing and sells at a discount, which is why benchmarks are written on light sweet barrels.
The contract's deliverable-grade specification lists several domestic and foreign streams that qualify, each with its own delivery-differential. A short choosing what to deliver picks the cheapest qualifying stream, which is the crude equivalent of cheapest-to-deliver.
Example: a medium sour crude with 24 API and 2.1% sulphur might trade $8 a barrel below WTI. On a 1,000-barrel contract that is $8,000, which is why grade specification is not a technicality.
Related: cl, cushing, brent, deliverable-grade, delivery-differential