“Formerly enslaved people disagreed over what freedom required”

This means they did not necessarily think:

“Freedom = simply not being owned.”

They could understand freedom more broadly.

For example:

Self-ownership

This means:

control over one's own person and labor.

Instead of another person deciding:

“You will work here.”

the formerly enslaved person could decide:

“I will determine where and under what conditions I work.”

Self-government

This means:

having the capacity to govern one's own affairs rather than being governed arbitrarily by another person.

At an individual level:

deciding one's household and economic affairs.

At a political/community level:

participating in political institutions and helping determine the rules under which one's community lives.

That is why “freedom” could mean much more to formerly enslaved people than merely:

“The law no longer recognizes you as someone's property.”