They are all words, and you can have su in there as well.
Tu is used to describe a possession of someone you address as tú, i.e. a singular person, informally. If you talk about multiple possessions of that person, you'll use tus.
- ¿Qué deseas tú para tu cumpleaños? - What do you wish for for your birthday?
- ¿Tú ya ha encontrado tus gafas? - Have you found your glasses yet?
Su is a bit more of a wild card. It can refer to the possession of él, ella, ellos, ellas, usted and ustedes. The same rule applies here, too: if the possession is plural, you use the plural sus.
- ¡Yo ama a su perro! - I love her dog!
- Por favor, laven sus camisetas. (ustedes) - Please wash your T-shirts.
Aidan, tu is the possessive form of tú, so it's the "your" that you'll use when talking to a person you address as tú. That usually means talking to a friend, a family member or a child.
Su is the possessive form for él, ella, usted, ellos, ellas and ustedes. So it translate as "his", "her", "their", and the kind of "your" that you'd use when talking to someone formally (usted) or when talking to multiple people (ustedes).