Not quite, what you are describing is the pH scale, although the two terms are related, according to the Columbia University document Acidity, Basicity and $pK_a$, $pK_a$ is
It turns that that the $pK_a$ of an acid is the $pH$ at which it is exactly half dissociated
The full derivation is on the document (and a bit long to post here with explanations).
But another explanation is provided in the document $pH$ and $pK_a$, where they state
$pK_a$ tells you if a given molecule is going to either give a proton to water at a certain $pH$, or remove a proton
So, to answer your question, in terms of $pK_a$, strong and weak acids and bases can be defined by the following table of examples:
Image source: Strength of Acids and Bases, a key point is that there is no clear boundary that defines strong from weak acids or bases.
They conclude with the following very generalised rule for $pK_a$:
For acids: the stronger the acid, the smaller the $pK_a$
For bases: the stronger the base, the larger the $pK_a$