SEM is a broader term than SEO, and is used to encompass different options available to use a search engine’s technology, including paid ads. SEM is often used to describe acts associated with researching, submitting and positioning a website within search engines.  It includes things such as search engine optimization, paid listings and other search-engine related services and functions that will increase exposure and traffic to your Web site. 
Comparing your Google Analytics data side by side with the dates of official algorithm updates is useful in diagnosing a site health issue or traffic drop. In the above example, a new client thought it was a switch to HTTPS and server downtime that caused the drop when it was actually the May 6, 2015, Google Quality Algorithm (originally called Phantom 2 in some circles) that caused the sudden drop in organic traffic – and the problem was probably compounded by unnatural linking practices. (This client did eventually receive a penalty for unnatural links when they ignored our advice to clean up).
Domain authority is an important ranking phenomenon in Google. Nobody knows exactly how Google calculates, ranks and rates the popularity, reputation, intent or trust of a website, outside of Google, but when I write about domain authority I am generally thinking of sites that are popular, reputable and trusted e.g. are also cited by popular, reputable and trusted sites.
Consider the length of your typical customer buying cycle. If your products and services have a short customer buying cycle, meaning your customers know what they want, search for it, and buy it, you may benefit from SEM ads that put your product right where customers will see it. Longer buying cycles, where customers research and compare for weeks or months, may not perform as well with SEM, as there isn’t an immediate buy after seeing one ad.
Google will INDEX perhaps 1000s of characters in a title… but I don’t think anyone knows exactly how many characters or words Google will count AS a TITLE TAG when determining RELEVANCE OF A DOCUMENT for ranking purposes. It is a very hard thing to try to isolate accurately with all the testing and obfuscation Google uses to hide it’s ‘secret sauce’. I have had ranking success with longer titles – much longer titles. Google certainly reads ALL the words in your page title (unless you are spamming it silly, of course).
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.
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