The US Constitution, Article IV, section 2. has two remarkably similar provisions in its second and third paragraphs:
A Person charged in any State with Treason, Felony, or othe Crime, who shall flee frlm Justice and shall be found in another State, shall, on Demand of the executive Authority of the State from which he fled, shall be delivered up, to be removed to the State from which he fled.
No person held to Service or Labor in one State under the laws thereof, escaping into another, shall, in consequence of any Law or Regulation therein, be discharged from such Service or Labor, but shall be delivered up on Claim of the Party to whom such Service or Labormay be due.
Now, if the governor of a state submits a claim that you are a fugitive from that state, you have the right to go up before a court and dispute that claim.
Whether that right extends to those claimed by private parties under the second paragraph, was a major source of contention during the decades preceding the Civil War.
The first federal law on the subject, passed in 1793, gave few of the protections. It even made no provision for habeas corpus, which has its own place in the Constitution.
As opposition to slavery spread throughout the north, states passed laws extending some of those rights. Some of them, including Pennsylvania, passed "anti-kidnapping" laws which punished slave catchers. The USSC found PA's law unconstitutional, but ruled that enforcing the law was the duty of the US, not of the states.
Considering how weak was federal law enforcement at that time, this was a serious impediment; states took to passing laws that their officers could not act to return escaped slaves.
As antislavery sentiment grew, northern abolitionists sometimes tooh to mob action to prevent return of escaped slaves.
In 1850, as part of a "compromise" between North and South over disputes that began about the admission of California as a free state and balooned, Congress passed the Fugitive Slave Law.
This bent much more to the Slaveowners' interests than the earlier law. While it did pass Congress, it was a bone of contention for the decade until the war broke out. Differences were both practical and philosophical.
Practically, defenders were seriously worried that any reliance on normal legal procedures would open the way to cheating on the part of abolitionists. So the law placed the burden of proof on the accused slave, but made no provision for a method of his proving his free-born status.
Opponents pointed out that slave-catcers brought imperfect descriptions, and there was no provision for checking after the man was handed over to the slave-catcher. He could go south with the "escaped slave" and then sell him as new property instead of returning him to the man who had advertised him as escaped.
Fingerprints were then unstudied, and slaves were neither photographed nor drawn. Advertisements for escaped slaves were frequently illustrated, but with stock woodcuts, not actual renditions.
Philosophically, if you have a claim against a person, then that person has a right to respond.
If you come into town and say, "That's my dog; he ran away last week," then somebody else can claim that dog, but the law has no provision for the dog to defend himself.
Thus the issue was whether negroes were persons or naturally property. The Constitution had said "persons" when it refered to slaves, but current southern feeling rejected that idea.
(Some slave states made a real effort to register "Free People of Color" so that nobody could claim that they were slaves.)