Should keywords be an exact match for Google to understand them?
No! Keywords do no longer need to be an exact match for SEO-reasons. Before you had to write rather annoying texts to perform as good as possible in organic search and could make the natural language quite difficult to read.
Today keywords should be chosen for what's relevant for your searches/visitors to your website. Try to inform the reader rather than the search engine - they have actually evolved quite a lot the last year.
Do not use keyword stuffing or the practice of showing as many SEO keywords as possible in a text or page. That procedure is not a long-term way to go anymore and are being considered blackhat in the Google world.
When you build the content and headers, then try to use a fluently text that makes sense for the reader and use synonyms to the key-word. The synonyms will help you build stronger content that will support your keywords.
Content is king.