down converter is mostly like mixer in analog circuits. after down converter, the signal central frequency has been changed ( from a higher frequency to a lower frequency).
down sampling is realized by decimation filter. what is changed in this process is signal sampling rate.
They are not same.
Down-converter refers to shifting the modulated signals spectrum to a lower centre frequency which depends on the a local carrier, the one of the input at mixer. This process doesn't change the spectral bandwidth.
Down-sampling refers to the decreasing the sampling rate of a signal. In this process the original signal's spectral bandwith will be reduced to avoid spectral aliasing and it depends on the decimation rate.
Down converters basically converts the signal into IF and then it goes to demodulator for further processing.
While in downsampling u reduces the sample rates and with this the sampling frequency decreases and to avoid alliasing u have to reduce the frequency of the signal (Nyquist rate).