If first degree polynomial models are linear models, why do results of linear model differ from that of poly(x,1)?

Question

As the title reads, the results from the linear and first degree polynomial model are different and I am not sure why. Any ideas why this might be?

linear_model <- nlme::lme(mpg ~ vs * gear, random = ~ 1 | ID, 
          data = mutate(mtcars, ID = dplyr::row_number()))
summary(linear_model)
             Value     Std.Error    DF    t-value   p-value

(Intercept)     8.378571    4.242762    28  1.9747918   0.0582
vs             -3.047802    9.300390    28  -0.3277069  0.7456
gear            2.316964    1.161928    28  1.9940684   0.0560
vs:gear         2.667651    2.423512    28  1.1007375   0.2804

poly_model <- nlme::lme(mpg ~ vs * poly(gear, 1), random = ~ 1 | ID, 
          data = mutate(mtcars, ID = dplyr::row_number()))
summary(poly_model)
                 Value     Std.Error    DF    t-value   p-value

(Intercept)         16.922377   0.978208    28  17.299367   0.0000
vs                  6.789161    1.512328    28  4.489213    0.0001
poly(gear, 1)       9.517902    4.773107    28  1.994068    0.0560
vs:poly(gear, 1)    10.958495   9.955593    28  1.100738    0.2804
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