inflammation of the brain and spinal cord and their meninges

this refers to a combination of "meningitis" and "encephalitis", see above

Inflammation of the brain and its membranes.

Inflammation of the membranes that cover and protect the brain and spinal cord. This condition sometimes occurs in patients with Behçet's disease.

An inflammation or infection of the brain and meninges

This is where both the brain itself, as well as the lining of the brain and the spinal cord is inflamed.

Meningoencephalitis is a medical condition that simultaneously resembles both meningitis, which is an infection or inflammation of the meninges, and encephalitis, which is an infection or inflammation of the brain. There are many causative organisms, including both viral and bacterial pathogens and parasitic microbes, which can give rise to meningoencephalitis along with other causative agents (such as certain antibodies). The disease is associated with high rates of mortality and severe morbidity.