모두 is primarily a noun meaning "all", "everyone", with some usage as an adverb too. 다 is heavily used as an adverb, and only occasionally used as a noun. 모두 has a narrower scope of meaning and usage, with no obscure usages. - 모두 여행을 떠났다: Everyone went on a trip. - 장관 인선은 모두의 관심사였다: The appointment of the minister held everyone's interest. - 이것 모두 가져가거라: Take all of these. - 이 모두가 나의 잘못이다: All of this is my own fault. 다 means "all", "without exception", and the like, but also has other obscure usages. - 올 사람은 다 왔다: Everyone who's supposed to come is already here. - 신이 다 닳았다: The shoes have worn out. (here it means "fully", a degree or an extent) - 사람이 다 죽게 되었다: This person is all but dead. (다 means "almost") - 그런 일이 다 있었어?: Did that really happen. (다 expresses "even that of all things!") - 잠은 다 잤다.: So much for sleeping. (다 expresses "no more") 다 as a noun: 내가 네게 줄 수 있는 것은 이것이 다이다: This is all I can give you (can't use 모두 here). 인생에서 돈이 다가 아니다: Money is not all there is to life (모두 may replace 다 here). So, 다 has a much wider and versatile application compared with 모두.

모두 and 다 can both be used as noun and adverb in sentence primary usage of 모두 would be as a noun, on the other hand 다 is more commonly used as adverb in daily usage there is not much of a difference between them, check korean dictionary for more information