shiranai simply means that I have never seen or heard something. wakaranai means that I tried to know or understand something, but couldn't. therefore, shiranai can be used as "I don't know," but not as "I don't understand." on the other hand, wakaranai can be used as "I don't know," and also as "I don't understand." but be careful: shiranai sometimes sounds kind of colder than wakaranai. "watashi no tokei ga doko ni aru ka shirimasen ka?" (Do you know where my lost watch is?) - "shirimasen" (I don't know, sounds as if "I don't care what happened to you") - "wakarimasen" (I don't know, sounds like "I wish I could help you, but I don't know about it") if you don't know which is better, i think wakaranai is often more suitable for many situations than shiranai.

I don't think shiranai can be used as "I don't understand". Maybe it's more like, "I don't understand at all".From what I know, usually wakaranai means "I don't understand" and shiranai means "I got no idea/knowledge/information". Shiranai is used when you got no information to answer the question asked. Wakaranai is used when you got some idea to the question but you don't know how to answer it. It's usually safer to use "wakaranai" if you're not sure which one to use because "shiranai" can be rude in some cases. Examples, If your friend asked you if you knew John. But you don't have any idea who that is. You would say "shirimasen". If you are on a road trip to somewhere with a group of friends and someone asked you if you're going to stay in a hotel or an inn. If you answered "shirimasen", it means you got no idea because you're not deciding or someone is deciding for you. If you answered "wakarimasen", it means you have not decided yet because you're not sure which one you should choose. If you are taking a class in quantum mechanics and you were asked to answer a question from last week's lecture but you don't know how to get the answer (even though you learned it before). You would say "wakarimasen". If you say "shirimasen" in this case, it would be rude. I think answering "shirimasen" vaguely means that you've not paid attention to the class so you got no idea. Hope that helps.