Bug and the corresponding story moves to next sprint

Did your team have any opinions on how to handle it?

I've worked with team's where we the functionality built could still work with little to no issues (so a very minor bug) and we chose to consider it done and open the minor bug as tech debt so we could get the functionality to market. 

Other times we've had things that were more of a showstopper and the work would be carried over because we couldn't comfortably consider the feature production quality. 

Am i suppose to move the bug and its corresponding story both to the next sprint?

Why would you do anything?  Why not let the team decide what to do?  There is no rule, suggestion, discussion of any kind anywhere in the Scrum Guide about this.  There are a lot of things that people have tried such as what @Tony Divel suggested. I worked on teams that have done similar to what Tony's teams did.  But it was never my decision. It was always the team's decision. Each and every occurrence was evaluated on the current situation to determine what actions would be taken. 

Ask your team what they want to do with this specific situation.  Next time it happens, ask them what they want to do with that one. Etc, etc, etc, ....

While testing one of the stories in QA,  the tester has found a bug however we are on the last day of the sprint. Am i suppose to move the bug and its corresponding story both to the next sprint?

or just the bug? and close the story with it in the same sprint and move the bug to next that starts from tomorrow.

It sounds as though there is product work that remains to be done. That's what the "bug" presumably indicates. Shouldn't this work be accounted for on the Product Backlog, so the Product Owner can account for it? It might be helpful to re-estimate the story to show the remedial work now thought to remain.