Obviously situations change depending on time, place, and the particular social conditions, but typically, when you use the term 'wage slavery', the implication is a situation where yes, technically the worker has the ability to quit their job whenever they want, but practically, they don't.
There surely is a distinction between even those forms of wage slavery and out right chattel slavery (or whatever), but the distinction isn't nearly as great, nor really, from a human stand point, really all that different. This is especially true the more 'brutal' the wage slavery gets.
Put it another way. Imagine you simply magically eliminated all forms of chattel slavery, but then immediately put all those magically freed ex-slaves in deep debt to their ex-owners (with heavy interest), and left them just as socially isolated as they are right now, and then gave them a chance to either take their chances and try to find a job somewhere else, or let them work off their debts to their ex-owners. Are they in a better position than they were before? Yes. Are they in anything remotely close to a good position? No.