- Mass or non-count nouns, that only have a singular, can’t be used with the indefinite article but often can with “some”, and which refer to “stuff” rather than “things”. These can’t have the same form for singular and plural because they don’t have plurals at all!
- Pluralia tantum, nouns that only have a plural form and no singular form. These are unit or count nouns like ‘normal’ nouns, but they can’t have the same form for singular and plural because they don’t have singulars at all!
Like Alex Lew I am gobsmacked by how many answers mistake what the question is asking about, and the grammar involved. Including from English teachers! There seem to be two confusions with other kinds of English noun, that don’t have both singular and plural:
Anyway, here are the mass nouns given in answers on this page as supposed identical singulars/plurals: furniture, luggage, rice, wheat, gold, silver, bronze, barley, oil, water, blood, sand, clay, wildlife, news, hair, learning, knowledge, change, spinach, beef, chili, spaghetti, macaroni, company [as in companionship, I presume], sunshine, rain, snow, shade, camouflage, Lego, underwear, money, graffiti, music, kudos, beer [can also be count noun].
And here are all the pluralia tantum: pants, scissors, blinds, goggles, panties, clothes, riches, jitters, shenanigans, remains, annals, suds, glasses, boxers [as in underwear], briefs [as in underwear], tweezers, alms, amends, cattle, doldrums, ides, pliers, shorts, smithereens, trousers, premises, jeans
A couple of suggestions are collective nouns that are ‘normal’ count nouns with singular and plural, but the singular can sometime be used with a plural verb: congregation, pair
And then there are just standard unremarkable count nouns: moustache, status
Finally there is some evidence of a singulare tantum, the opposite of plurale tantum, in the word shambles. This is a count noun, it can follow the indefinite article, it’s used with a singular verb, yet it has no plural.