Dari, Persian and Tadjik languages all come from one source, but historically the modern Afghanistan was included in the region where some peculiarities in comparison with the literature Persian appeared, so that's how Dari now differs more from Persian than from Tadjik. For example, Dari has got two long vowels o and e, which Persian lacks, and uses two archaic diphthongs, ai and aw. Dari grammar has a complicated system of aspects and tenses of the verb. The vocabulary also differs from Persian and is closer to Tadjik.
Dari used to be very conservative, and the language of aristocracy in the beginning of this century was sometimes not understandable fro ordinary people. After Afghanistan was proclaimed a republic, the popular language became more important in social life, and literature forms changed a little.