1.) cognitive decline or loss in 2 or more spheres of cognitive function (e.g., memory, judgement, calculation, language, spatial orientation; not memory alone);
2.) that said cognitive decline is stable or progressive over a period of 6 months or more;
3.) that the cognitive decline is of sufficient degree as to interfere with social or occupational function.
Dementia of Alzheimer type is merely the commonest of the dementias. There are other types, such as Frontotemporal Dementia, Subcortical Dementia, and Vascular Dementia, as well as mixtures.
(FWIW, we cannot actually speak entirely accurately of Alzheimer's Disease without having a tissue diagnosis, via biopsy or necropsy, showing senile plaques and neurofibrillary tangles. It is more precise to speak of Dementia of Alzheimer type, otherwise, when a patient's dementing illness shows the features commonly identified with Alzheimer's Disease during life.)