Justin is a married man and Britney has a boyfriend and twice divorced. It has been over 12 years.
I HIGHLY doubt there is anything between them. They were basically kids then and now 30 something year old adults. Its just the way those awards work. They come and go as the show progresses. No one stays the whole time.
They just need to be cordial with one another and set a better example. This is kinda ridiculous tbh. It's pretty obvious that Justin still has issues by the way he followed Ellen around to avoid being alone.