The short answer is that ™ is supposed to mean someone just thinks something is a trademark. ® is supposed to mean that a government trademarking authority has agreed that it could be a trademark and has issued a registration certificate.
Getting your trademark registered by a government trademarking authority always takes time and money. It is fitting that at the end of the process, if you are successful, you will receive a certificate that looks almost like a graduation certificate. In the United States, the paper certificate bears a gold embossed seal. And you deserve it! You spent time, money and often had to prove to skeptical bureaucrats the worth of your brand.
If you jump through these hoops, it can be irritating to see others wrongly proclaim that their trademark is registered with the registration symbol ® when they have not. But you can only take action against this misuse if you can prove the symbol misuser did so deliberately–that it intended to deceive or mislead the public or the USPTO. This can be tricky to show.
For example, last month the Trademark Trial and Appeal Board dismissed an opposition in which the owners of two similar trademarks (FACETS versus PHACET) fought over which one used and had the right to register its trademark for software. The company applying for the FACETS registration had successfully registered FACETS for several types of services but had not yet been granted a registration for the trademark in connection with software (the trademark had been registered a number of years ago for software but that registration had expired). Despite that, it used the registration symbol with the trademark In SEC filings to describe not only its services (correctly, since they had registered) but also its software (allegedly fraudulently because FACETS was not currently registered for software).
SEC filings are sworn statements but that’s not enough to make them evidence of symbolic fraud in the TTAB’s eyes, at least in this case.