They can't be used interchangeably most of the times.
The basic difference is this:
The number 1000 has 4 figuers (=digits). If your salary is 100 000 dollars, people say you get " a six-figure salary". The number 25 has two figures ( 2 and 5).
an official number representing an ammout is usually called a figure. For example you talk about unemployment figures or trade figures.
Also, " a figure of 50 million dollars" simply means 50 000 000 dollars.
In all other cases, we use the word "number". For example , Waiting in a bank, you wouldn't hear : " Figure 35, to counter 5." * It would be number 35.
Also, room number 406. Buliding number 2 ( or just Building 2). Member number 234, article number 14 etc.