Please explain what differences are there in the (human) immune response to a viral infection vs. a bacterial infection?

Short answer: It depends on the individual organism. For example some viruses trigger the immune system to mount a cytotoxic cellular response in which the infected cell is killed. Some bacteria are killed directly by antibodies in conjunction with the complement system. You usually can't differentiate viral vs bacterial infection based on how you feel or what it looks like in the case of a throat infection.