Problem: In this passage priests and Levites are not distinguished from each other, but in other places they are (cf. Lev. 1:5, 8, 11; Num. 6:23).
Solution: When several things are kept in mind, the problem disappears. First of all, the priests were also Levites, all being sons of Aaron.
Second, in Deuteronomy, Moses is speaking in general terms to the whole nation and thus avoids the finer distinctions.
Third, some 38 years separate the two passages. It may be that the earlier distinction was no longer in general currency after the wilderness wandering.