trend parameter in ARIMA

[SK]

Hi, 

I'm trying to understand how the "trend" parameter affects the coefficients in the ARIMA model. Example dataset:

ts = np.array([1,1,3,2,2,5,5,6,7,6,9,10,11,15,11,14,16,15,16,19,23,24,25,24,27,28,28,27,24,27,28,29,33,32,34,37,39,40,39,43,49,46])

m1 = ARIMA(ts, order=(1,1,0)).fit()
m1.summary()

                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.0351      0.135      0.261      0.794      -0.229       0.299
sigma2         5.6271      1.446      3.892      0.000       2.794       8.461

m2 = ARIMA(ts, order=(1,1,0), trend='t').fit()
m2.summary()

                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
x1             1.1251      0.269      4.190      0.000       0.599       1.651
ar.L1         -0.2741      0.162     -1.693      0.090      -0.591       0.043
sigma2         4.1145      0.884      4.652      0.000       2.381       5.848

m3 = ARIMA(ts, order=(1,0,0), trend='t').fit()
m3.summary()

                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
x1             1.0151      0.029     34.495      0.000       0.957       1.073
ar.L1          0.6616      0.164      4.044      0.000       0.341       0.982
sigma2         3.6783      0.724      5.083      0.000       2.260       5.097

I thought trend='t' would be equivalent to fitting a constant to the differenced data, so shouldn't m2 and m3 show equivalent x1 coefficients?