While reading section 4 of chapter 20, I am confused between Temporary inital selection and time selection. Can we not say temporary initial selection is a type of time selection?
Not quite - initial is all around a specified event happening to all members, at a particular age, for example, they all buy a policy at the same time. This is selection at the very start of a policy, and can usually mean different mortality/morbidity characteristics compared to the whole population at the very start. Time selection is the idea that mortality/morbidity varies with calendar time, for example there is now a better chance of picking up cancer cells earlier on, compared to 30 years ago. So this is 'selection' across a whole group of people, which is across a wide time span, not just at the start.