You know I'm bad at communication/ It's the hardest thing for me to do

Title from "The Wire" by HAIM

Today my friend and I were chatting in her car on the way to Stratford and she started talking about friends. She talked about how high school was rough for her, and that she felt like she didn't have a lot of friends. At first, this was shocking to me, because she's the kind of person who, after having one conversation with you, will deem you her friend. But as she continued to talk, I could see that they way she classifies friends varies significantly from the way you or I would. She went on to say that she has best friends, but then the people who most people would consider friends, she considers mere acquaintances. For her, a big part of friendship is seeing the other person, definitely more so than for me. Obviously seeing your friend contributes a lot to your relationship, but it soon became clear to me that she took the amount of time spent together as a direct indication of your friendship. She said that she didn't consider one of the girls in our group of four to be her friend. And not as in "you can't be my friend any more", but rather that she felt their relationship was fading away.
She clearly thinks about relationships and friendships more than I do. It's true that we haven't been able to hang out with our one friend for a while because of a variety reasons, but I wouldn't say our friendship with her is anything less than it was a couple months ago.
She had her birthday the other week, and quite a few people were not able to make it to her party. Some had legitimate reasons, others simply backed out at the last minute. Especially because she likes birthdays so much, this affected her quite a bit. She had hoped that by not putting a lot of effort or thought into planning the party (she simply asked people to hang out at a pub), that she wouldn't be as affected by it, but she was. So clearly this has been on her mind for a while if she was thinking about it before planning her party.
It's times like these that I wish I was more socially attuned to what to do in a situation like this. Obviously she needs comfort and reassurance, but I'm not great at providing that. I don't know how to. I tried, because I felt so sad that she thought I was her only friend. And while I wasn't able to completely reassure her, I think I did help a bit. I told her that we're all friends and that I enjoy hanging out with her. She feels things very deeply, so that meant a lot to her.
I was going to bring it up to the other two friends in our group, that she was feeling a bit down and it would be good if we could hang out all together. But then she said that I wasn't to tell anybody about what she said. While I understand her desire to keep her feelings and thoughts between us, it makes it a lot harder to try and help her. And I'm sorry I've betrayed her by talking about it here (although no one involved in the story knows about this blog), but I felt so helpless knowing this information, so I had to do something with it.