Personal Line of credit: You retain the entire equity stake but pledge assets or the equity in a company for a loan. This is essentially a form of secured borrowing, but no exchange of equity.
Levered Recap: This is usually an exit strategy. An outside buyer buys a stake from you, usually a majority stake (60%–80%) with the implicit agreement you stay for a few years until they buy the rest. In a good levered recap the buyer brings on a “CEO in waiting” to learn the business, your market, etc.
So one doesn’t transfer any equity and the other transfers the majority of the business. You do the math.