The two words 빨간 and 붉은 (both in the adjective form) are interchangeable in many contexts. The basic difference between the two words is that 붉은 is used for something that is always red by nature, and 빨간 is used for something that is more specific and individual.

For example, your lips are always red, so it's more natural to say that they are 붉은 입술. But if you make them even more red by putting on lip stick, you can say that they become 빨간. And for objects like pens or notebooks, they can be in any color but if they are red, that is more often called 빩간 than 붉은.