If you want a simple distinction between the two words, then cure is to eliminate a health problem altogether, and treat is to mitigate a health problem's ill effects, or improve a person's wellbeing living with that condition.
cure
1. (tr) to get rid of (an ailment, fault, or problem); heal
treat
5. (Medicine) (tr) to apply treatment to: to treat a patient for malaria.
Collins English Dictionary
However if you want to get more nuanced the distinction may be less strong. The application of a treatment may result in a cure, and it may be said that a patient is treated and discharged (for all you know they are cured from the treatment). That's why I say in some cases "treat" can mean "cured", but strictly speaking the distinction is the one I mentioned above.
Coming to your question about curing or treating high blood pressure, that depends on whether the person's blood pressure can be brought to a level that is no longer considered "high"; in that case they are cured. Otherwise the prevention of an exacerbated condition, or the maintenance of the current level would be treatment without elimination of the problem altogether (cure).