You know that in English there's the we/us which means the same thing. Only that you use we in the start of the sentence and us when it's at the end. On the "tu/ti" case, tú is a personal pronoun which works as a subject. However, when tu is not accentuated it becomes a possessive so it always requires a noun after it. Ex: Tu casa y tu perro (your house and your dog). Ti is another pronoun which it's always used at the end of the sentence and it doesn't accept a noun after it. In order to use para tu... it needs a noun to make it correct and it will always require something before too. Ex: Vas para tu casa?

Ti: pronombre personal. Se emplea en los comprementos con preposición. Es un regalo para ti → It's a present for you No podría vivir sin ti. ¿ a ti qué te parece ? Tu: adjetivo posesivo. Es un regalo para tu padre → It's a present for your father. Han venido tu tía y tus primos → your aunt and your cousins have come.

TU: Adjetivo posesivo (no puedo reemplazarlo por el nombre de una persona ) ejm: tu coche ≠ juan coche TI: Pronombre ( se puede reemplazar por el nombre de una persona ) ejm : un regalo para ti = un regalo para juan

Tú--se usa en el sujeto. Tú estás haciendo la acción. (Tú is a subject pronoun, you use it if "you" are doing the action...you drive a nice car, you walk to work, you eat dinner late, etc...) Tu--sin acento o tílde=your. Tu coche es azul=Your car is blue. ( tu without accent =your / possessive ) Te--pronombre directo e indirecto. Te voy a llamar...Voy a darte el libro.( indirect pronoun ) Ti--se usa con otros preposiciones. Este libro es para ti...Estoy alegre por ti...( with other prepositions)

Tú (with the stress/emphasis in the 'u') is an equivalent to 'you' in english or 'thou' in the Early Modern English (As 'Ti' is an equivalent to 'Thee'). So, 'Tú' and 'ti' are very related, but not the same. Also, be very careful with "Tú" and "Tu", because the first mean "you", but the second one means "your".