“Latino”, (or the feminine “Latina”) signifies someone whose native language is related to the Latin of Ancient Rome. It includes speakers of Spanish, Portuguese, and Italian, as well as French and Romanian. “Hispano” or “Hispana” refers to to people who speak Spanish, whether of the Iberian variety, or any of the dialects now spoken throughout the New World. Both terms are often hyphenated with the suffix ‘-Americano’, signifying someone from the former Spanish colonies in the Americas. The two terms are often used interchangeably. Among Spanish speakers, “Americano” means “from the Americas” (North or South), NOT “from the United States of America”. After all, there is a United States of Brazil and a United States of Mexico as well as a USA. The formal name for a citizen of the USA is “estadounidense”. Informally, they are sometimes referred to as “Norteamericanos”, regrettably lumping in Canadians.
I was brought up in a Cuban family in a Cuban ghetto in a North American city. We always referred to ourselves as Hispanos or Latinos, again, interchangeably, and sometimes Hispano-Americanos or Latino-Americanos, to underscore we were not truly European Spaniards but from the Americas. I don’t know what people of other Latin American origin call themselves, but I suspect it is the same. If we needed to distinguish ourselves from other South Americans, we just said “Cubanos”. Other countries in the region often have nicknames for their compatriots, Puerto Ricans sometimes informally call themselves Borinquenyos, (after an ancient Indian name for their island), Costa Ricans call themselve Ticos, and so on.
The important thing to keep in mind is that other than speaking variants of a mutually understandable language, the Spanish speaking peoples of the world have little in common with each other. They are as culturally distinct as the Irish, English, Welsh and Scots are. In fact, Yanks, Canucks, Aussies, Kiwis, Jamaicans, Bahamians, Caymanians, Belizians, Bermudans etc are also culturally distinct, to varying extents, in spite of similarities in their speech they inherited from the British Empire.
There is no such thing as “Latinx”. It is just another annoying example of the exasperating Anglo tendency to lump together everyone or everything they don’t understand into a convenient catch-all linguistic category. As for the -a or -o suffix used in the Spanish language to indicate gender, get over it. Spanish, like most languages in the world, uses gender-marked nouns. Gender is used to vary the sound of the spoken language to make it less monotonous, the gender of a noun has nothing to do with its masculinity or femininity. For example, when referring to a handgun, “La pistola” is feminine, but “El revolver” is masculine. The word for rifle is masculine, but the term for shotgun is feminine. Whether a word is masculine or feminine is completely random. It has nothing to do with misogyny, or lack of it.