Difference between AR model and distributed lag model

[Ara]

Hi,
I was trying to estimate the number of lags of y to be included in an estimateion by looking at its correlogram. I dtermined that it follows a path of AR(2) model. Then if I specify in the equation ar(1) and ar(2) along with the independant variable, then the coefficients of ar(1) and ar(2) are different than if i specify the lags as y(t-1) and y(t-2)? Aren't ar(1) and ar(2) same as y(t-1) and y(t-2)? Also, what is then the difference if I choose ARDL model instead of ARMA model in E-views if it is just an AR(2) model?

Thank you for the help.

[Bablowski]

I think the difference is caused by the estimation method and this depends on the version of your software. Simple lags y(t-1), y(t-2) are estimated by OLS method but AR(2) is estimated by ML method.

ARDL model contains not only lagged dependent variables but also independent variables in level and its lagged values.