The Grateful Dead pioneered freewheeling two-set shows and developed the stereotypical travelling fan community, both of which are also in evidence at Phish shows.

Common aspects of the music include... (though note also how the music differs.)

Common aspects of the community include colorful clothing, public drug use, relative affluence, and geographic diversity irrespective of any given performance's actual location.

However, the Grateful Dead did not pioneer group improvisation (jazz did), fan taping and trading of performances (bluegrass did), drug use, or other things that happen to be common to both groups. Phish and the Dead draw on common elements, and the Dead combined a subset of those before Phish - but the two actually differ quite a bit.

"The Dead are the Dead. They were the forerunners, and are. They were on a certain level probably the most influential band on this era of music, the p.g.e., post-grunge era. ... They crossed it [jazz, as in Miles Davis' A Tribute to Jack Johnson] over to rock, in terms of experimentation on stage, and lifestyle, and music as a community, and all kinds of stuff."
-- Trey Anastasio to Addicted to Noise c.6/95