Trans generally means a man born in a woman’s body or a woman born in a man’s body. People who are trans prefer to be treated as the gender they are inside, whether or not they appear to be that gender externally, just like traditional men would take offense to being referred to as she or her. It’s fine to see people as just people but you should acknowledge that you wouldn’t want to be referred to as the wrong gender and neither do trans people.

Two-spirit appears to be more of an umbrella term for native American third genders, with no single general meaning. The third gender part appears to be important, meaning they are neither male nor female on the inside, regardless of what gender they may appear to be. Take this with a grain of salt since this is the first time I’ve heard the term and just looked it up. There appears to be some contention around the meaning, so I’m probably wrong.