You're most certainly correct. The aforesaid definition doesn't encompass all psychopaths, as not all psychopaths act criminally.

These definitions are quite difficult to explain and have been debated since they were conceived. So I'm just going to give you the cliffnotes version...

Primary psychopaths: Primaries are the unfeeling type, the "true psychopaths", if you will. I use "unfeeling" loosely, as we can experience shallow emotions, such as agitation. These lot are mostly the product of nature. However, environmental factors can trigger psychopathic behaviour and/or influence how the psychopathic behaviour manifests.

Secondary psychopaths: ... are almost entirely the product of their environment. They are deemed "pseudo-psychopaths" because they lack the low anxiety and callousness psychopaths are known for. But they are still considered psychopaths because they got a 30 or higher on the Psychopathy Checklist (PCL-R). Of these two types, secondaries are more likely to commit violent crimes and/or become habitual criminals. It's been theorised by one expert (whose name escapes me) that secondaries feel guilt constantly, a result of severe and chronic childhood abuse or neglect.

ASPD: Antisocial personality disorder is basically a wastebasket term for habitual criminals. It covers a wide range of mindsets, from a generally good kid who got caught up in gang activity to an actual psychopath. But, for the most part, antisocials are essentially secondary psychopaths who didn't quite get that 30+ score on the PCL-R. Most were simply socialised into a criminal lifestyle or were subject to abuse as children.

I suppose anything is possible, but I highly doubt it.

Dexter, no. Lila, iffy. Miguel, probably.