I created a jsfiddle here: http://jsfiddle.net/z5SEp/
The events for latest Chrome seem to be:
mousedown
blur
mouseup
click
Although I could not find any documentation to rely on, it would make sense to me that blur is fired after mousedown, but before mouseup. Mousedown causes blur, but you could leave your mouse button down for an extended period of time and still cause a blur.
The order of click events will always be 1. mousedown 2. mouseup 3. click. The blur makes sense to be after mousedown but before mouseup.
More things to keep in mind
If you trigger the button click like this: $('button').trigger('click');
, then the blur event will not fire, and focus will remain on the textarea.