As
@Chicken Man posted, both the Grateful Dead and Phish crossed into the Jam Band genre. Both bands were a fusion of multiple styles.
However, the music and lyrics in those two bands are not particularly similar. The Grateful Dead had some poetic, artistic help writing song lyrics. Phish lyrics can be silly or trite.
I’ve seen both bands live, the Grateful Dead twice with Jerry and Phish twice in the early 2000’s. I’ve also seen Dead and Company a couple of times as well as The Other Ones.
The GD with Jerry was off their game the first time I saw them in December at Compton Terrace, Phoenix 1990. They still had some excellent moments at that show. I saw them again in Denver Colorado the following year and they were fantastic the whole show.
Phish were great musically both times I saw them play live. They put on a good show.
The Grateful Dead has the better songs. It’s not even close for me in that regard.
Phish has had interesting musical concepts over the years. Then, I watched and heard them play a tiny desk concert in recent years and I thought it sucked.
Trey Anastasio (guitarist/singer), member of Phish, has played with various members of the Grateful Dead over the years. He played with Phil Lesh and friends and Dead & Co. In the clips of Trey I’ve seen with Dead & Co, I noticed that Trey’s voice had a similar, paper thin, quality which reminded me of older Jerry Garcia.
When Jerry was a young man, I thought his vocals sounded sublime. I still liked his voice as he aged but, to me, it lost something. I can’t help but think drug addiction played a part in changing his vocals.