When you say something is 'sparse,' you mean there isn't much of it and what there is, is unevenly distributed.
For example, when you talk about sparse vegetation, you mean that the vegetation is thin rather than thick, and that is spread out across a vast region. Or there is some greenery, but not everywhere.

Thanks to the sparse traffic, we managed to cover the distance in two hours.

Why he wastes so much time on his sparse hair is beyond me.

`Scarce', on the other hand, suggests that the shortage of the commodity is temporary. It is not permanent. Scarcity can be man-made as well. For example, usually in our country, the day before the budget, petrol becomes scarce.

I understand that during the Second World War, chocolates became scarce.