The most significant differences are in quantity and materials. Discrete manufacturing can be done one item at a time, and the product can later be dismantled into separate parts. Process manufacturing tends to produce large quantities at a time, and the product can’t be separated into individual ingredients again.
A good example would be the process of making sandwiches. The sandwich is put together discretely — you can make a sandwich at a time, putting together the bread, mayo, and cheese. But the ingredients themselves are process manufactured — you can try to separate the bread back into flour, eggs, and water, but you will probably fail (and make a big mess).