Circular vs Linear Convolution
Convolution in DFT is still circular.

Think of the DFT as taking the 1st period (in time and in frequency) of the DFS (discrete Fourier series). In DFS, both the time sequence and the frequency sequence are N-periodic, and the circular convolution applies beautifully.

I personally think all properties in terms of DFS, and then consider the 1st period when speaking DFT.