slip vs curve last

Slip and Curved are not related.

Slip lasted shoes don't have a semi-rigid board glued onto the top of the midsole, on which the insole rests. If you take the insoles out of a slip lasted shoe, you'll see nylon stitched at the center of the midsole. Slip lasted shoes are usually more flexible in every way.

Curved last refers to the shape of the shoe when looked at from below. Curved shoes curve toward the big toe, and are (or used to be) sometimes called banana lasted shoes. Straight shoes are shaped almost like light bulbs, with no curve toward the big toe. Semi-curved shoes (no surprise) are somewhere in between.

Generally, the faster you're going to run in a shoe, the more curved it should be. There are notable exceptions to that observation, though. Joan Benoit raced plenty fast in very straight, but light, racing shoes to win the 1984 Olympic Marathon.

Some people have flatter feet, and to them, straight is generally better no matter what. Others have higher arches, maybe pronate less, and prefer curved lasts.