Shouldn't the zero-inflated negative binomial and hurdle-negative-binomial be different?

inflatable-hurdles.R

library(pscl)

y = c(86, 0, 29, 0, 16, 0, 20, 0, 0, 1, 2, 0, 0, 96, 0, 7, 0, 0, 
0, 0, 25, 0, 0, 233, 0, 7, 0, 0, 67, 0, 6, 0, 0, 0, 12, 0, 0, 
0, 9, 0, 12, 18, 39, 0, 59, 15, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
0, 88, 48, 50, 26, 0, 47, 0, 0, 0, 18, 0, 60, 0, 0, 180, 0, 0, 
28, 95, 13, 0, 28, 19, 32, 0, 2, 0, 0, 0, 28, 0, 0, 0, 184, 14, 
0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 6, 21, 68, 0, 0, 0, 3, 9, 0, 
0, 0, 1, 15, 0, 13, 26, 0, 0, 0, 0, 0, 0, 0, 0, 342, 93, 0, 3, 
0, 0, 0, 94, 0, 0, 56, 56, 27, 11, 27, 7, 0, 12, 66, 0, 0, 3, 
2, 0, 30, 0, 0, 0, 5, 6, 0, 116, 0, 82, 173, 53, 0, 8, 0, 0, 
0, 0, 396, 0, 0, 0, 0, 0, 0, 0, 8, 0, 69, 4, 55, 17, 9, 0, 4, 
4, 0, 0, 1, 0, 0, 0, 0, 24, 0, 36, 38, 17, 147, 0, 156, 0, 0, 
0, 0, 5, 1, 91, 0, 112, 73, 0, 0, 0, 25, 0, 162, 9, 184, 11, 
51, 72, 1, 0, 0, 26, 0, 92, 0, 5, 0, 0, 12, 0, 163, 0, 0, 0, 
6, 0, 0, 15, 0, 0, 320, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 12, 0, 2, 83, 17, 0, 0, 116, 0, 0, 0, 16, 0, 0, 0, 
0, 5, 0, 0, 0, 164, 26, 35, 3, 0, 11, 46, 0, 0, 0, 0, 0, 0, 0, 
56, 139, 5, 0, 1, 0, 48, 1, 0, 183, 0, 0, 110, 12, 41, 0, 0, 
0, 0, 0, 1, 13, 0, 136, 13, 0, 9, 10, 1, 80, 148, 0, 0, 18, 52, 
7, 16, 16, 0, 0, 0, 0, 1, 0, 11, 0, 0, 51, 76, 0, 0, 13, 0, 9, 
0, 79, 0, 0, 8, 17, 0, 4, 157, 0, 0, 257, 0, 1, 20, 0, 0, 18, 
1, 109, 0, 4, 41, 0, 65, 0, 3, 0, 12, 151, 61, 11, 15, 0, 693, 
41, 0, 46, 0, 26, 0, 0, 7, 0, 0, 2, 0, 0, 0, 0, 0, 625, 0, 1, 
34, 12, 10, 0, 44, 2, 0, 115, 217, 0, 0, 0, 0, 14, 0, 18, 2, 
13, 22, 0, 0, 0, 20, 0, 0, 35, 34, 0, 22, 0, 3, 0, 0, 2, 148, 
0, 0, 21, 0, 0, 88, 37, 55, 0, 0, 0, 0, 0, 183, 0, 0, 83, 0, 
0, 0, 0, 75, 0, 0, 21, 0, 0, 0, 0, 3, 0, 0, 2, 0, 37, 118, 0, 
8, 1, 0, 38, 0, 0, 0, 114, 47, 0, 224, 7, 0, 0, 0, 97, 0, 0, 
26, 0, 0, 0, 43, 0, 65, 308, 11, 14, 38, 0, 0, 0, 2, 0, 9, 59, 
0, 0, 54, 26, 0, 1, 40, 1, 15, 81, 0, 124, 0, 3, 0, 1, 0, 6, 
69, 320, 26, 0, 0, 116, 0, 0, 10, 0, 0, 0, 0, 62, 1, 0, 0, 0, 
138)


hurdle_model = hurdle(y ~ 1 | 1, dist = "negbin")
inflat_model = zeroinfl(y ~ 1 | 1, dist = "negbin")

# Identical coefficients and likelihoods?
coef(hurdle_model)[1] - coef(inflat_model)[1] # 3e-9
AIC(hurdle_model) - AIC(inflat_model) # 0