I would argue that there is a difference. If you think of 노래 as 'song,' and 곡 as 'track,' it's not too hard. They are used almost the same ways as the English equivalents of the words. For example, when referring to specific songs within an album, it could be more appropriate to use the word 곡 if both speakers in the conversation are familiar with the album. There are lots of examples that I could give you, but I'd rather you just let me know what you're curious about. 어떤 질문도 있으면 꼭 코멘트해주고 제가 빨리 답장하려고..

Technically same, but very different in spoken language. You would almost always only hear 노래 in spoken language. I only see 곡 in dictionary and maybe academic writing. Beginners should focus on what is actually spoken, which comes with experience.

roughly 70% of Korean words from Chinese character; 노래=곡(曲)