Same taxonomy in two content type I have two content types Blog and Stay which use the same taxonomy Location. I have two or more posts use same term Cyclades. 

Is it possible when a user clicks on a Cyclades term link in a Blog post to only show posts from Blog content on the taxonomy page? Likewise, when a user clicks on Cyclades in a Stay post, to show only Stay content on the page?

I know i can create two different taxonomy for each content type, but I dont want this solution.
You can have same taxonomy being used by multiple content types. 

You can achieve this by using 2 options
1. Overriding node.tpl.php for the taxonomy page. Here you can create two separate tpl files specific two different content types.
2. Create PAGE display of VIEWs and pass "type" as an argument. Based on this argument you can always display the teasers belonging only to the desited "Content Type."

Option # 2 is little easier from implementation point of view whereing Option # 1 though could little time consuming but will be better from performance perspective.