TM is used to signify common-law rights in a trademark pursuant to the Lanham Act. Thus, those who have not yet registered their brand name with the United States Patent and Trademark Office (USPTO) should list a ™ instead of a R. The same goes for those applications submitted but not yet accepted. TM is typically used to protect an unregistered mark by alerting potential infringers that a term, slogan, logo or other indicator is being claimed as a trademark. However, the use of TM does not guarantee the owner’s mark will be protected under trademark law. To succeed in a common-law infringement action under the Lanham Act, the trademark owner must prove: 1) s/he was the first to use the trademark and 2) the infringing party’s use of the trademark confuses the public from distinguishing the goods’ source.
The R symbol denotes a trademark which has been registered with the USPTO. The use of the symbol may only occur after the USPTO registers the mark. Registering your trademark gives you superior rights over others in the U.S. to use your trademark in your industry, and it provides you the ability to obtain treble damages against infringers. Not only will a registered trademark deter imitators, it also provides you with a heavy presumption of ownership in the courts. Because a registered trademark is much more preferable over an unregistered trademark, I invite you to take a look at a past answer I provided to “How do I register a trademark, such as company name?”
The "C" with a circle around the letter, or the use of the word "copyright," gives notice to the public that the work is copyrighted and that you own the work. However, the C symbol is no longer required to protect your work as it's automatically protected when the work is created. To learn some more on copyrights, check out Stanford University’s amazing Copyright and Fair Use Center.