Apple - Open website without actually opening it in browser from terminal

You can use curl

curl https://www.google.co.uk/

and if you don't want the output

curl --silent https://www.google.co.uk/ > /dev/null

Curl and Wget can be used to call a website, but if you are wanting to mimic some function on the website then these wont accurately mimic a user running a request in a browser.

Browsers have engines in them that process css, javascript and html that's why you have to use them.

If you want to use a website as if a user was using the site through a browser without opening the browser you should look into some headless testing frameworks such as PhantomJS, otherwise browserstack a browser testing platform has an api you can access, this will still open a browser tab but in a cloud vm somewhere so no on your actual machine.