The "TM" stands for trademark and the "SM" stands for service mark. They indicate that the person is claiming a common law form of trademark protection in goods or services. Only those who have obtained a registered trademark or service mark with the U.S. Patent and Trademark Office are allowed to use the "R" in a circle, which indicates that theirs is a registered trademark.
These marks are a form of shorthand that tell the public that a product or service comes from a certain source. We are surrounded by these marks. For instance, if you see the mark of "Apple" you most likely think of mobile devices like phones. And if you see a swoosh design , you likely think of athletic equipment. Both of these are very "strong" marks and are therefore accorded a high level of protection by federal trademark law. Other types of marks are merely "descriptive" of the product or service being offered. An example could be "Brite" Cleaners. Descriptive marks are not as strong as the "fanciful" or "arbitrary" marks referred to above. For that reason, they may not be eligible for federal trademark protection.
As long as you continue to use the mark in connection with your business or enterprise, then it can remain a valid mark. (There may be periodic registration requirements with the USPTO to maintain a federal registration.) Even if you sell the rights to the mark, as long as it continues to be used in connection with the business, the mark can continue to exist. This differs from copyright protection which has a set period of time and then the underlying work loses protection and becomes part of the public domain for anyone to use.
Almost anything can be used as a trademark, as long as it does not become generic (meaning that it describes the product or service, such as what happened to the term "aspirin" which at one time was a trademark but became the word used to describe the type of medicine). It is best to let your imagination play with the idea for a mark and not settle on obvious connections. The strongest marks are those of made up words or fanciful associations. Here are some examples of famous trademarks: