Here's an example of a service mark with which I hope most of you reading this are very familiar.
The distinction between "trademark" and "service mark" is that the former is for goods, and the latter is for services. In common usage, "trademark" covers both terms, but technically a protected mark for a service is a service mark, not a trademark. For example, if you're selling, say, shoes and put your company logo on the shoes, that's a trademark. But if you're providing a service, like, say, running a science fiction convention, your convention name and logo are service marks.
Trademarks are indicated by the character ™ — the superscript "TM." This is conveniently a built-in character in the Windows character set and has a "named" HTML shortcut.
Service marks are indicated by the character ℠ — the superscript "SM." There's no Windows character for it and you have to use the HTML numeric code (8480).
These two symbols are typically used to designate trade/service marks that have not been registered with the appropriate government agency. In the USA, that agency is the US Patent & Trademark Office. Within the EU, the agency is the EU Intellectual Property Office. Other countries have their own agencies, and there are national agencies within individual EU countries as well, but these are the two with which I've had to deal in my WSFS MPC Chair role.
EU registration gives you coverage in all of the member states. For example, WSFS (through a non-profit corporation named Worldcon Intellectual Property controlled by the MPC) registered the most important marks (Worldcon, Hugo Award, and the Hugo Award logo) through EUIPO in 2016. Registration was finalized just before the Kansas City Worldcon, meaning that Worldcon 75 was the first Worldcon held in Europe covered by the registered mark, and Dublin 2019 will be the second. This was quite timely, as there was an attempt to set up a different "Hugo Award" (not for SF, and as far as we can tell, they were unaware of the WSFS Hugo Award) within the EU in the past year. The MPC/WIP was able to negotiate an agreement with the presenters that allows them to give out a prize that recognizes the Hugo (not Gernsback) they want to honor without causing potential confusion with the WSFS mark. I think that having EUIPO registration was a contributing factor in our ability to negotiate that agreement. Conversely, a long (and annoyingly expensive in terms of solicitor time used) discussion with a certain German luxury fashion design house means that Worldcons are enjoined from every making articles of clothing with the name of WSFS's premiere award on them. (We could use the logo, but not the words identifying what that award is.)
Unregistered marks are those that you assert protection over but that have not been registered. For example, SFSFC Inc. (parent non-profit corporation of this year's Worldcon in San José) asserts a service mark on the bridge-and-map logo that we originally used for ConFrancisco, the 1993 Worldcon, and that we currently use as the SFSFC corporate seal.
If your mark (either trade or service) has been granted registration, you can use the ® symbol — a specific form of circle-R, sometimes approximated by (R) if you don't have access to that symbol. It's appropriate (and indeed recommended) to use this symbol when you have registration; however, using the TM/SM symbol is okay as well, as far as I have been able to determine. What you should not do is use ® when the mark is not registered.
What appears to be a bit fuzzy is the use of the ® for an international-scope event like Worldcon. For example, while "Worldcon" is registered in the USA and the EU, it is not registered anywhere else, including countries that have hosted multiple Worldcons such as Canada and Australia. Even though the majority of Worldcon members are likely to live in the USA and EU, I would think it unwise to use ® for a Worldcon being held outside the registration area. Because having to use different mark symbols depending on where the convention is held would be a great way to cause more confusion, the Hugo Award Logo incorporates only the ℠ symbol. We do not think this erodes our service mark.
Another fuzzy area seems to be the incorporation of a mark within a mark. For example, the words "Hugo Award" within the Hugo Award logo are a service mark on their own. As it happens, it's only the rocket that is covered by mark assertion for the logo; the words "Hugo Award" are registered generally, not specifically in that typeface. Where this gets even more complex is the case of "Worldcon" being within the name of another convention. Both the 2018 and 2019 Worldcons have the word "Worldcon" within their logos, which is reasonable, and both conventions can legitimately claim intellectual property (service mark) protection for their logos. But remember that each Worldcon committee is a legally independent entity. WSFS doesn't "own" the Worldcon committees, nor do those committees "own" the WSFS service marks. (The committees do have representation on the MPC, so they have a "share" in the ownership during their term.) So how do we reconcile the use of one mark within another?
My own theory on this is that Worldcon is similar to how Olympic committees are independent of each other but have the right to hold the Olympics and use intellectual property that belongs to the International Olympic Committee. For example, the various Olympic Games incorporate the Olympic rings symbol. Worldcon committees have, in effect, a limited non-transferable license from WSFS to use the WSFS service marks (Worldcon, Hugo Award, etc.) for the purpose of holding a World Science Fiction Convention. This includes the right to sub-license it for certain functions (Sales to Members is typically under this arrangement), but not to sell those marks because they don't own them. Consequently, the next two Worldcons can claim service marks on the Worldcon 76 and Dublin 2019: an Irish Worldcon logos respectively by their own parent organizations, but they can't claim IP ownership on "Worldcon" itself or otherwise use their licensed marks for any purpose other than holding the Worldcons they they've been authorized to run.
Something you don't need to do, and indeed really shouldn't do because it's silly, is to use one of the mark symbols on every single usage of the mark. You don't go around writing, say, Coca-Cola® every time you say you bought a Coke®, and not even the Coca-Cola Company would say that you should, as long as you're using the words to describe their actual beverage. Similarly, don't go around writing Hugo Award® and Worldcon℠ over and over just to be cute. But conversely, don't use the WSFS marks to describe something they aren't, and also, use the Hugo Award Usage Guidelines and the actual Hugo Award logo when you want to illustrate something that talks about the Hugo Awards. Don't use random images you can find by doing a Google Image Search on "Hugo Award" just because you personally like that design better. (Those images are from artists whose logo proposals were not selected by the MPC when we developed the logo, and in theory are there to allow those artists to display their work as exposure for them.) Using non-official Hugo Award logos actually hurts the Hugo Awards and Worldcon by eroding our intellectual property and creating confusion. So when it comes to writing about the Hugo Awards, accept no substitutes!