Within a set of positive numbers, a number is small if it is close to zero. A number is smaller if it is less than another number.
Within a set of positive and negative numbers there is ambiguity, because being closer to zero does not correspond to being less, but to being less in absolute value. Depending on context a negative number may be called "smaller" if it is closer to zero, or if it is more negative.
This article deals with positive numbers, and is also applicable to negative numbers by taking the absolute value.
Small numbers are numbers that are small compared with the numbers used in everyday life. Very small numbers often occur in fields such as chemistry, electronics and quantum physics.