Google doesn't offer SEO services. Remember, Google is a search engine and they have created their own algorithm for positioning websites. If Google offered SEO services, you would basically pay to be at the top of search results, since they would know exactly what to do on your website to get there. Smaller businesses, those that don't want to spend money on PPC, can use Google's non-Google Ads tools to optimize their searches.
Comparing SEO or Google Ads, formerly known as Adwords, is like comparing apples to oranges; both help put your brand on the SERP in front of potential customers. By now, you have a good understanding of what SEO is and how it differs from running a Google Ads campaign. There's no cost to appear in organic search results like Google's, and making changes to improve your website's SEO can have a big impact on your search rankings over time. Translating your high CTR from your AdWords account to your organic search snippets can pay huge dividends, as an increase in organic search CTR will not only directly drive more traffic from your existing rankings, but can also help improve your rankings, creating a flyer effect where you get even more traffic.
The basic principle you should understand here is that the case of SEO VS Google Ads, as in the case of organic VS payments in general, is the case of time VS cost. Google has SEO experts who can guide you through the process of improving your site's SEO, but you can also do it on your own. SEO, in this case, is mainly focused on optimization for Google, since most searches are performed on it. If you want to be at the top of the search results on the first page like next week, Google Ads is better for you.
In AdWords, keywords are the phrases you're targeting, while search terms are the phrases people type in Google. In fact, Google has confirmed many times that PPC ads through Google Ads won't directly help your SEO performance (i.e., your organic search ranking). Which means it won't appear if the search term isn't related to your keywords, plus, no matter how much you pay, your ad won't show before someone else's if your website has more organic matches to the search term. If you include too many search terms that don't seem to be connected in any way, Google will mark your website as misleading and decide to ignore it completely, which means it won't show up in searches (even if your intentions aren't deceptive and really honest).
Instead, Google Ads can help you show your ads to potential customers, at the exact moment they're looking for a company like yours.