Asymptomatic refers to a state of no symptoms at a particular time.  One can be asymptomatic in the incubation period, and/or, in the period following the infection as shown by positive rtPCR which shows that an infection is present.  It doesn't mean that they'll remain asymptomatic forever.

Presymptomatic means during the incubation period for the virus and you have no symptoms. 

> The antibody serosurveys getting underway in different parts of the country add further evidence that a good number – possibly anywhere from around 10 percent to 40 percent – of those infected might not experience symptoms.

And in this context, it meant the person remained asymptomatic throughout the whole infection.

https://www.sciencealert.com/a-physician-answers-5-questions-about-asymptomatic-covid-19