What is the difference between set notation and interval notation?

Interval notation explicitly uses inequality symbols to present the domain or range of particular function.

An example would be ##x>0## for a logarithmic function.

Set notation uses brackets to provide restrictions on your function. So the same domain ##x>0## can be written as (0,∞ ].

The square brackets simply mean that the value nearest to the square brackets are included in the solution set.