Aren’t all three essentially the exact same thing?
How I understand it:
Income Generation: short call to receive the income generated when the market is not going to provide you with capital gain return
Improving on the market: Market is likely to be flat, so you benefit from the TV of option that is likely to expire, by receiving the cash flow (income)
Market Realization: your stock is not going to get to where you need it to be, so you use the Cash flow to add return
Covered call to manage risk? How does a covered call reduce risk of a portfolio
Lowers vol of a portfolio, provides income, and allows some additional upside. Negative would be during a rising market you might get called away, which is the difference between the strike and IV of the call sold.
Of the three motivations for a covered call strategy I’d say 1 and 2 are quite similar (income generation, improving on the market). In my Wiley notes they add that improving on the market could also be interpreted as capturing the time value of the option if it expires worthless, which is a bit different from pure income generation. Nr. 3 (target price realization) is straightforward, if you want to lock in a certain price (just upside), set the short call strike price to your target price.