Ischemic Stroke: This is the most likely diagnosis given the sudden onset of right-sided weakness and slurred speech, which are classic symptoms of a stroke. The symptoms suggest a left hemisphere stroke, which can affect motor control on the right side of the body and speech, given the left hemisphere's role in language processing for most individuals.

Hemorrhagic Stroke: Similar to ischemic stroke, a hemorrhagic stroke can present with sudden focal neurological deficits, including weakness and speech difficulties. The key difference lies in the cause (bleeding vs. blockage) and potential for increased intracranial pressure.
Transient Ischemic Attack (TIA): Often referred to as a "mini-stroke," TIA presents with similar symptoms to a stroke but resolves within 24 hours. It's a warning sign for a potential future stroke and requires immediate medical attention.
Seizure: A seizure, particularly a post-ictal state (after a seizure), can sometimes present with focal weakness and speech difficulties, although these are typically accompanied by other seizure symptoms.

Brain Tumor: Although less common, a brain tumor can cause sudden symptoms if there's a hemorrhage into the tumor or if the tumor causes a seizure. Missing this diagnosis could be fatal due to the potential for increased intracranial pressure and brain herniation.
Subarachnoid Hemorrhage: This condition, often due to an aneurysm rupture, can present with sudden severe headache and sometimes focal neurological deficits. It's critical to diagnose promptly due to the high risk of rebleeding and poor outcomes if not treated.
Meningitis or Encephalitis: Infections of the brain and meninges can present with a variety of symptoms, including sudden weakness and changes in mental status. These conditions require urgent diagnosis and treatment to prevent serious complications and death.

Multiple Sclerosis (MS): MS can present with a wide range of neurological symptoms, including weakness and speech difficulties, but these are typically more gradual in onset and accompanied by other symptoms such as optic neuritis or sensory deficits.
Mitochondrial Encephalomyopathy, Lactic Acidosis, and Stroke-like episodes (MELAS): A rare genetic disorder that can cause stroke-like episodes, among other symptoms. It's considered in younger patients with recurrent or atypical stroke presentations.
Cerebral Vasculitis: Inflammation of the blood vessels in the brain can cause stroke-like symptoms, among other neurological deficits. It's a rare condition that might be considered in patients with systemic symptoms of inflammation or autoimmune disease.