A stroke is analogous to a heart attack in that the patient is experiencing an area of ischemia and infarction in the brain. This can occur as a result of a ruptured blood vessel or a clot. This ischemia can be local to a small area in the brain (generally from a small clot) or a larger area in the case of a bleed or a series of clots.
You should consider a stroke anytime you have a patient with an altered mental status in the absence of any parts of STOPEATS (other than pressure since this is related to bleeding or edema). Specifically, if there is no mechanism of trauma (source of bleeding) or cause for edema like a toxin or altitude injury.
A stroke is serious and needs treatment in a hospital. Treat them as you would a patient with increased intracranial pressure because that is what they are. Just like with a TBI, do not give a patient with a suspected stroke pain meds—since you do not know if the cause is from bleeding, you cannot take the risk of giving something that would increase bleeding.