How to separate links from buttons?

I am struggling with how my users don't understand the difference between buttons and links.

There are currently my LINK-buttons (external actions - e.g. opening a new page or opening a new page with a popup)

"create new" link

and BUTTON buttons (internal actions - e.g. opening an popup on the page)

various buttons

and there are inputs (that looks quite similar to a button, but has a lighter background)

input

  1. Is the difference understandable and logical?

  2. Do you think people will click on a link and know that a new page will open or will extend a "show more" box?

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