"That famous band records a new album."
Translation:그 유명한 밴드는 새 음반을 녹음합니다.
I think in some earlier post @McPwny has explained the differences to me. Can only hope that I understand them correctly.
(1) 새, adjective (determiner) meaning brand new, unused
(2) 새로운, derivative adjective from the verb form새롭다.
새롭다 = 새+롭다
-롭다 / -럽다 are suffixes usually attached to foreign nouns to change them to adjectives. (Equivalent of the -ic, -ive, -ful etc. adjectives in English).
새롭다 is just one of the exceptions where -롭다 is attached to an adjective. 새롭다 means to be like new / to carry the characteristics of 'newness'.
The difference to '새' is '새로운' carries that subtle meaning of "different from before" while '새' means "not existed before".
새 음반 = new album (recently released, not heard before)
새로운 음반 = re-released album / another (not necessarily new) album
In common usage, as you pointed out the 2 expressions are used almost interchangeably. Still it's worth noting the difference.
All comments are welcome.