What's the difference between LineString and Multipoint in GeoJSON

A LineString is a Polyline or from Wikipedia "a curve specified by the sequence of points". So if you like to do a track or route based on latitude and longitude for a map application - use LineString.

MultiPoint is simply a collection of points without lines between them. Say a group of people. So the use cases are very different.

Specification of LineString requires at least two positions.

Other than that there is only a difference in intent. LineString defines a line through the points in given order. MultiPoint defines a finite collection of points.