Popular prejudices about schizophrenia and general ignorance about borderline get in the way of thinking straight about the differences. But there's a reason why borderline is a personality disorder and schizophrenia is a condition. Schizophrenia, for all its horrors, is like the flu: you can get it and one day, you don't have it. Borderline, on the other hand, is far more deeply embedded in your psyche.
(And yes I know these terms can be vague and loose. But so is the term omelet. Yet if you've eaten a few, you can tell the difference between one and scrambled eggs.)
(And yes, I know that these things have degrees. Not everyone with borderline acts on murderous envy.)