In other words, are all these uses incorrect?
It is true that both words refer to something that can be parametrised, although parametrise is not taken in the exact same sense.
In mathematics and physics, parametric means that something can be controlled by a finite set of parameters. Often, you can make choices for this set of parameters, e.g. the plane can be parametrised by abscissa and ordinate of points, or by the distance and bearing angle relative to some origin. But you will not introduce new possibilities by doing so, it is just another set of controls for the same thing.
In technology and IT, parametrisable (also spellt parameterisable, parametrizable, parameterizable) means that values that would by default be regarded as unalterable constants can optionally be turned into tunable parameters.
It makes sense then that different suffixes are used: -ic to describe the state of something being controlled by parameters, -able, able to be parametrised.