When used to mean world, мир and свет are synonymous, though the latter can sound somewhat poetic and is more often used in literature and set expressions than in day-to-day life. For example:
Ничего
на светелучше нетуЧем бродить друзьям
по белу свету
Or to quote the Russian national anthem:
Одна ты на свете
There are other situations where the two cannot be substituted for each other. For instance, one can't use свет when talking about the world of ______
«В мире животных»
В мире политики.
Of course, both words also have other meanings which are entirely unrelated (e.g., peace and light).
Also note that мир is used with the preposition в, whereas свет is used with на
Ни за что
на свете!Что
в миренеизменно?