How to close the search toggle for vscode?

Similar to what Vijey has mentioned, you can use the Toggle Panel keyboard shortcut which will do the job for me. On A mac the shortcut is ⌘ Command+J

I'm coming from sublime where the search results appear in a new tab - making it much easier to close the results (just like closing an other tab)

Your search results are appearing in the panel, not the sidebar.

To toggle the panel:
pc/mac: ctrl + ` (backtick)
mac: ⌘ + J

However, if you want your search results to appear in the sidebar (which I think is the default behavior), then add this line to your settings:

"search.location": "sidebar"