@trevlee11,
In Latin there would be no difference between the two phrases; definite and indefinite articles are not used in Latin. (This often makes it difficult for English speakers when translating from Latin. For example, there's no way to tell whether it should be "He met the Devil" or "He met a devil.")
But, in either case, rough translation of living either 'the' dream or 'a' dream would be
vivens somnium.