Contestation

contestation means a situation in which the meaning, scope, or practical implications of a concept are challenged, disputed, or struggled over.

So you can have both:

A. Contestation between understandings

Former slaveholders might understand legal freedom primarily as:

“The person is no longer my property and can enter a labor contract.”

Formerly enslaved people might understand freedom more expansively:

“Freedom should enable me to control my labor, establish my family independently, acquire property, and build an independent livelihood.”

That is a difference in the content assigned to freedom.

B. Contestation between legal freedom and material reality

Formerly enslaved people could also say, in effect:

“The law says we are free, but without land, capital, and sufficient bargaining power, much of the freedom that emancipation promised cannot be exercised fully.”

So these are not competing explanations. Both can be part of your meaning of “contested.”