Hispanic refers to people of Spanish speaking origin. It is a linguistic marker. It was coined by/during the Nixon administration and because of this it is seen as "top down" naming. It is problematic for many people (myself included) because it infers that what is important about these people is their proximity to Europe (ie whitness) and points directly to their colonization. Not only that but it doesn't take into account the people from "Hispanic" countries that don't speak Spanish, but instead still communicate through their indigenous languages.

Latino is shorthand for Latino Americano. Latin American. It is a geographic marker instead of a linguistic one. It refers to a place, a space and not a language. In contrast to "hispanic" which is an example of a name for a people coming from an institution, the term comes from the people themselves. You are much more likely to here "hispanic" from people more closely tied to white institutions (government, the justice system, etc.) and "latino" from those closer to grass-roots movements or community based organizations.

As my homie BSR quoted above, Spanish is a very sexist language so folks tied to more intellectual circles have started writing 'latin@' and more recently latinx to be more inclusive of both women and gender non-conforming peoples (which in the case of the muxes of southern Mexico, for example, have long been apart of our societies and cultures.

I would say that Latinx is the safer word to use (the word me and mines prefer), but you will find people on both (and other) sides of the discussion and who prefer different terms. You should ask them how they identify.