Consider:
Down 4 b informal : to or toward a place that is thought of as below or away from another place
A1. She drove down to our house.
A2. Come on down and see us sometime.4 c : to or toward a place that is away from the speaker
A3. He is heading down to the store.
A4. Would you mind moving (further) down so that we can sit here, too?
&
Up 4 b informal : to or toward a place that is thought of as above or away
from another placeB1. She went up to the cabin for the weekend.
B2. How long will it take to drive up (to their house) and back?
B3. Come on up and see us sometime.5 a : to or toward a place that is close to someone or something
B4. I walked up to her and said “hello.”
B5. Please pull up a chair.
B6. He lay down and pulled the covers up.
I find these definitions very interesting. It seems using down or up makes no difference to the examples in both 4 b when altitude doesn't need to be taken into consideration. Is it true?
However, as for 4 c and 5 a, I might think it's a little bit different.
For A3, I suppose both up and down work just fine and make no difference in meaning.
For A4, I suppose using up wouldn't make sense as moving-up only helps to make things worse.
For B4, I have a gut feeling that using down isn't as good as using up, but I cannot explain why.
For B5, firstly, I don't know whether the speaker is asking the addressee to pull the chair to the speaker or the addressee or either of them depending on the context. Second, I suppose using down would mean the opposite – being away from the speaker; the same is true of B6.
Is my understanding correct? Please help to clear up my confusion.
Best Answer
With go, or verbs that can be interchanged with go, such as drive, walk, move, etc., sometimes the relation between the destination and speaker can be expressed with either verb.
Do we consider the store "down" or "up" from us? Assuming the store is not significantly downhill/uphill from you, it doesn't matter too much. In my opinion, "down" may have a bit of meaning of "forward" or "in front of," - something I've commonly heard is "I'm going to walk down this path" when you really mean "I'm walking forward along the path."
Conversely "up" will have a bit of meaning of "behind." This isn't really a hard and fast rule and could vary widely depending on region.
The implication in using either word is that a bit of a journey was involved or will be involved.
Native speakers would understand either way, unless the "X" in "I went down/up to X" is physically higher or lower than you. Saying "I'm going down to the third floor" when you are on the second floor will confuse people. Saying "I'm going down to the restuarant" will not.
In A4, assuming a situation of theater seats where they are all in a row (none are really "up" or "down") - you could substitute "up" and not really change the meaning, though "down" sounds more natural.
Regarding 5a, "up" or "up to" can also mean "near," particularly with words that involve the subject moving items (pull up, push up), or the subject moving himself/herself/itself ("up to" will be used - ran up to, walked up to, etc.)