Definition of some: An unspecified amount or number of: "I made some money".
Definition of a little: Small in size; Short in extent or duration.
I'd say both sentences have a differing meaning of the quantity of milk spilled.
A little milk was spilt. Implies a small quantity.
Some milk was spilt. Implies an unknown amount of milk was spilled. (Would require further context, but even with that context unknown, the sentence meaning is still different.)