If Toy Story was real, and you had a Buzz Lightyear toy, would it think it was a space ranger or would it think it's the toy from the movie and will try and find its way back to Andy, amirite?

It would think it was a space ranger unless it had realised it was a toy then it would always try find its way back to me I guess. 乂ᵒ◡^乂

IfToy Story was real, and you had a Buzz Light Year toy...would you claim to think for it? Yup. SMGDH

OP asks the real questions

...*looks at original buzz and woody toys in closet

The latter.

Look at the shoe. If it says Andy then find Andy and give the toy back. If not it's your toy.