Tür und Tor
What's the difference?
"Tür"="door", "Tor"="gate". For very big doors (like garage doors - 'Garagentore') there is some overlap.
You might also want to add that "Tür und Tor" also is an idiomatic expression. If you open the floodgates to sth. bad, dann öffnest du etw. schlechtem Tür und Tor.
Tor is also goal, for any football (soccer) fans. I presume it is similar in other sports, but it is definitely "Tor" in football
- Die Tür (the door) is often inside or at the entrance of a house - die Schlafzimmertür, die Haustür
- Das Tor (the gate) is often larger and somewhere outdoors - das Gartentor, das Garagentor, das Burgtor
- Das Tor (the goal) is where to score in soccer or hockey, in basketball it is der Korb (the basket)
There is an interesting subtlety in your examples for Das Tor (the gate), as in English we would say "the garden gate" and "the castle gate," but we would say "the garage door" rather than "the garage gate."
Well, the small entrance to the garage designed for humans is "die Garagentür", while the big entrance at the front designed for cars is "das Garagentor".