Difference between a VAR and a VECM


I am performing cointegration analysis using Eviews and the DOLS estimator in the cointegrating equation. After saving the residuals of this equation (they are stationary then the variables are cointegrated), I estimated the short run equation including the lagged error term, one lag of the dependent and independent variables taken in differences (my sample is not large), and a constant. I got the coefficients of the VECM. However, I was thinking that in this case that I have included only one lag, if I estimate an unrestricted VAR including the dependent variable and the independent variables and the estimated error term, the coefficients of the VAR should be EXACTLY the same of the VECM that I estimated. The only difference is that when estimating the VAR, I will get also the equations considering the independent variable and the error term as dependent variable. The result was that the coefficients were extremely similar, but NOT EXACTLY the same. Why do this happen?