Wavemenu 1-D Wavelet and DWT behave differently

I am trying to decompose a signal into its Daubechies Wavelet components, in particular db2. I require an 'a trous' decomposition, that is the coefficients must be of the same length as that of the signal. However, the DWT function gives the usual sub-sampled result, and hence I tried using the wavemenu GUI, which happens to provide an 'a trous' implementation by default.

However, I require the analyze the results and its implementation (eg. to check causality and filter coefficients). I noticed that even if I sub-sample the results generated by the wavemenu GUI, it does not match the results given by DWT. This is causing a lot of confusion and I'm unable to identify the algorithms used for implementation in the 'a trous' version.

I have already searched a lot in the documentation and other websites, and I would be grateful if the MathWorks Team or anybody else could clear this for me. For the purpose of reference:

% Signal 'x' is of length 16
% aprT is the approximation coefficients given by the wavemenu tool for 'db2', has length = 16
plot(0:15,aprT);
hold on;
% app is the approximation coefficients given by dwt(), has length = 9
[app,~] = dwt(x,'db2')
plot(0:2:16,app);
% Shouldn't the coefficients be the same!