In this case, the denotation is very close to the connotation. The root of patience is pati, coming from the Latin word patientia, meaning "suffering. In fact, in Latin, the word pati means to suffer or pain.
In addition, the word patient can be either a noun or an adjective. The adjective came first (mid-1400s), describing to a person that is able to suffer enduringly without complaint. The noun form appeared in the late 1400s, referring to a person suffering from a medical condition. In order to heal, one must first endure suffering.
Now that is an interesting concept. When we are sick, our immediate response is to suppress the symptoms, as we don't want to feel the pain or discomfort. However, the symptoms themselves tell us that something within us is moving, which is a key to healing. Think about it: if your nose is runny, that means the mucus is trying to escape. If you keep coughing, it's because toxins are attempting to eliminate your lungs and throat.
So, if you can take the suffering, you are a patient person. And in the long run, it will make you stronger.