Is it normal for two friends to act this way?

Y'know usually I'm rather oblivious to these kind of things, but I'm curious to see if other people have seen or have relationships like this with their friends.

So I recently started hanging out with some friends from college more as a group. I've known this one girl for a while know and her friends and I all just clicked.

Last night we were all out and about eating at Denny's. I've know Desi for almost two years now and last night her best friend since like preschool was with all of us. And I noticed that her friend (who is also a girl - idk if that matters) was acting rather attached and possessive.

Every time Desi mentioned something or even when she didn't her friend had a remark about some story about them when they were younger. Or how Desi would always do this or that, and she understands her so much.

It was weird, I'm not really one to notice these kinda things too much, but her friend seems kind of on edge to prove how close they were and even got this weird look in her eyes too.

All the while, Desi seemed to be totally immune to her friends ways. It wasn't just me who noticed it, but everyone else seemed to let it pass (since this is only like the 4th or 5th time I've met Desi's friend).

Not only that but Desi seemed to be a bit more reserved than she usually is. Like her friend did most of the talking. But she seemed unfazed by her odd behavior of her friend and didn't seem to see anything out of the ordinary.

Maybe it was just me. I asked another friend Cara who was there and knows both of them and she says, they're just like that and shrugged it off.

Have any of you seen or are maybe in a kind of friendship like this? Or is this new to you guys like me?