One thing to understand about the catching of slaves - at least after the Fugitive Slave Act of 1850 - is that in a lot of situations, catching the right person was not the primary concern. Even prior to 1850, free black people out in the world were sometimes kidnapped into slavery, as Solomon Northup describes in his account of his time in bondage:

I felt of my pockets, so far as the fetters would allow—far enough, indeed, to ascertain that I had not only been robbed of liberty, but that my money and free papers were also gone! Then did the idea begin to break upon my mind, at first dim and confused, that I had been kidnapped. But that I thought was incredible. There must have been some misapprehension—some unfortunate mistake. It could not be that a free citizen of New-York, who had wronged no man, nor violated any law, should be dealt with thus inhumanly. The more I contemplated my situation, however, the more I became confirmed in my suspicions. It was a desolate thought, indeed.

Northup is visiting Washington, and is drugged at a pub, shackled, and eventually ends up in Louisiana. His kidnapping was in 1841, nine years before the passage of the Fugitive Slave Act as part of the compromise of 1850. When the Fugitive Slave Act was passed, though, it included the following provision:

That when any person held to service or labor in any State or Territory, or in the District of Columbia, shall escape therefrom, the party to whom such service or labor shall be due, his, her, or their agent or attorney, may apply to any court of record therein, or judge thereof in vacation, and make satisfactory proof to such court, or judge in vacation, of the escape aforesaid, and that the person escaping owed service or labor to such party... And upon the production by the said party of other and further evidence if necessary, either oral or by affidavit, in addition to what is contained in the said record of the identity of the person escaping, he or she shall be delivered up to the claimant, And the said court, commissioner, judge, or other person authorized by this act to grant certificates to claimants or fugitives, shall, upon the production of the record and other evidences aforesaid, grant to such claimant a certificate of his right to take any such person identified and proved to be owing service or labor as aforesaid, which certificate shall authorize such claimant to seize or arrest and transport such person to the State or Territory from which he escaped.

Essentially: if you, a slave owner, go before a judge and provide a sworn affidavit that a black person you see on the street is your slave, and you can convince a judge that this is the case, the judge will release that person into your custody and you can take them with you. "Satisfactory proof" is left to the discretion of the judge.

As you can imagine, this caused some consternation in free states with any kind of black population, leading to posters like this one that warned all black people to be aware that this was happening, and this one meant to rally support for people that this was actually happening to. Which makes sense - if a person doesn't see the wrong in owning a human, why would that person care about which specific human was owned as long as someone was doing the necessary job?