Small refers to the size of something.

A small boy

A small drink

Little can refer to size also, but it can also be used to describe other things. It can describe the idea of size. It can describe the idea of nothingness.

A little worm.

The worm was very little compared to the elephant.

Someone might say to another person: "Your ideas were of little use to me."

This implies the idea were worthless.

There was very little juice is the carton, so I threw it away.

This means there wasn't enough juice left to make it worth saving.

Often used interchangeably by some speakers.

But

Small = of a size or amount that is less than usual.

Little = more often used to describe an extent or degree of something.

A small car or a little car both are OK

Little

used to emphasize how small an amount is.

"I have little doubt of their identity" correct. means you are sure of their identity.

"I have small doubt of their identity" incorrect wrong.

"I have little doubt in my mind" correct = you are sure - certain

"I have a small doubt in my mind" correct = you are almost sure -almost certain with a tiny doubt

it is something that you will have to acquire over time with practice and exposure to the language.

In 98% of cases you can probably interchange the two words.

@John I would interpret the statement ‘I have a small doubt in my mind’ to mean that I have reservations about it, I’m not sure.

As you say. ‘I have little doubt in my mind’ clearly indicates certainty.

English can be a very confusing language at times !

I am not an english teacher, but you can see this way: Small is small, the opposite of "big", ok? And Little is like a small amount, small quantity, a portion, the opposite of "a lot" or "too much/many"

Examples:

A golf ball is smaller than a soccer ball.

Don't put too much salt in your pasta, just a little is enough.

Thank you all for the comments!