Little or a little?

A little child.

I am making a little progress - a small amount of progress. Positive. At least I'm making a little progress.
I am making little progress. Negative. However hard I try, I'm making little progress. Not much. Only a little.

How do I explain the difference?

A little is a short for one, an amount.

In the second sentence little modifies or reduces
Glass half full and glass half empty.

Little or small?

 Small and large.

Little and big.

Short and tall.

Large size.

Small size clothes, small, medium, large.

You can say a tiny little, but not a small little.