What is the difference between the approximation signal (say a4) & the one obtained by plotting the coefficients obtained by using the code wavedec & appcoef? why the waveform for a4 in DWT toolbox have same no: of samples as the original signal?

I am new to wavelet analysis and tried understanding its concepts. Not sure if this is a valid doubt but surely would be thankful for clarifications.

[C,L]=wavedec(x,4,'db8'); D=detcoef(C,L,4); A=appcoef(C,L,'db8',4); plot(A)

By doing the above code the no: of samples will be around 500 as the original signal is having around 8000 samples. But by using the wavelet toolbox by typing "wavemenu", & then doing DWT the plot we get for a4 has the same no: of samples as the original signal. Is the waveform seen from the DWT toolbox and the one obtained by writing the above codes same? Because both look similar but have different no: of samples. Also what does the y-axis of the plot represent?

Thankyou.