Is Naegleria fowleri the same as amoeba?
In general, "brain-eating amoeba" is a common term for amoeba protozoa, so they refer to the same thing. Detailed analysis is as follows:

Once amoeba protozoa enter the human body through the nasal cavity, they invade the central nervous system along the olfactory nerve, especially attacking and damaging brain tissue. They multiply rapidly and cause primary amoebic meningoencephalitis. Initial symptoms in infected individuals may include headache, fever, and vomiting, followed quickly by paralysis and coma.
In daily life, one should avoid swimming, diving, or washing the face in untreated natural water sources such as ponds, rivers, and hot springs, especially avoiding getting water into the nasal cavity. When using a nasal irrigation device, only use water that has been boiled and cooled or a specialized nasal rinse solution. Household water-related devices such as water heaters and humidifiers should be regularly cleaned and disinfected to prevent the growth of amoeba protozoa.