English originally had a familiar form thou and thee but it became obsolete and is only found in old literature and old prayers. So, the English you covers familiar singular form, plural familiar form, Singular formal form, and formal plural form.
In much of Brazil, seu is used most of the time. In Portugal, both are still used. and still in some of Brazil. The familiar form, when it is used, is for very close friends and family and with children. The formal form is more respectful, so you don't have to guess if it is okay to use it. Which is why, I think, it became the only currently used form in English and why it is so well used in Brazil.
If you have family or close friends in Portugal, they are likely to tell you that you can use the teu form with them if you use the wrong form. After all you are close to them!
But if you use the teu form with someone who is not close to you, that person may feel slightly insulted that you would dare to not use the respectful term with them when they do not even know you that well.
On this website, they teach both because seu can also mean their and you plural. In Brazil dele is used for his and dela is used for her, but originally seu could also mean his and her and I am not sure if it may still be used that way in Portugal
. The teu form is always singular you masculine, familiar form. The seu form is singular formal masculine. Directly above ThanKwee has posted the link for the possessive pronoun CHART which includes teu and seu. Feminine would be tua and sua. and plural teus or tuas and seus or suas. They agree with the noun that they are modifying in gender and number.
Higher up I posted other charts which don't even include teu forms because Brazil rarely uses them and they add dele for his and dela for her. Dele, deles, dela, delas must really be for his, her and maybe for their depending on locality. The chart directly above is the standard and perhaps closer to Portugal. The others were added later and deal more with Brazil. I would love for someone Portuguese to speak up and specify which chart is best for which area.
I am from California. There are a lot of people from Portugal in my area, so I want to learn to talk to them. There are some people from Brazil too.
There is a difference between Portuguese for Brazil and Portuguese for Portugal.
It is not equivalent in English either. When talking you might use either one, but "your horse" is a phrase in which "your" is a possessive adjective modifiying a noun and "the horse is yours." is a sentence with a verb and in which "yours" is a possessive pronoun used as a predicate nominative which does refer back to the subject. When learning a language, we need to learn which is which.