Your styleguide says it is ‘select’. The whole world says ‘click’. You are confused. So am I. I have tried being informal while writing instructions: “Hit the Submit button to complete regiustration.” But they spanked me for being so casual and changed ‘hit’ to ‘select’. You know, no one reads manuals. Now I know why.
We “click” all buttons and links. Why? Because the mouse makes a “click” sound when we do so. Why do you want to “hit” your mouse? What has it ever done to you???
Why do we “select” options and check boxes? Who knows?