A continuity family is Teletraan I: The Transformers Wiki's term for a group of distinct but closely-related individual continuities. For example, Generation One, the original Transformers toyline and franchise, had several separate continuities. Therefore, there is no single Generation One continuity, but many related ones. Further, these continuities are clearly distinguishable from the various Unicron Trilogy continuities, or from Robots in Disguise.
There are, at this time, five known major continuity families:
There is also one minor (i.e., much less prominent) family:
Generation One is by far the most extensive continuity family in the Transformers multiverse. It includes the original toyline and all related media, the divergent Japanese exclusive material begun in 1987, and the Generation 2 revival of the franchise from the 1990s, as well as later "rebooted" versions of the Generation One story, such as those created by Dreamwave and IDW. Additionally, the so-called "Beast Era" also belongs to this continuity family. This includes Beast Wars, Beast Wars II, Beast Wars Neo, and Beast Machines.
This family had 17 years of exclusive reign, encompassing all material that was produced between 1984 and the end of Beast Machines in 2001. Even after the establishment of other continuity families beginning in 2001, the rate at which Generation One fiction has been produced is almost equal to that of non-G1 fiction. It also includes by far the largest number of micro-continuities.
Although RiD's original, Japanese incarnation -- Car Robots -- was initially presented as part of this new family, Car Robots has since been retconned into a part of Japan's Generation One continuity family. (See Continuity#Unified Japanese continuities.) Good luck figuring that one out.
This includes the Armada, Energon, and Cybertron toylines and all related media. Japanese incarnations are included. Initially, the Japanese version of Cybertron (known as Galaxy Force) was not part of this family, but has apparently been retconned back in. (See Continuity#Unified Japanese continuities.)
This family's central feature is the 2007 live-action film Transformers and any sequels. Accompanying the movie is a large array of supporting fiction in the form of prequels, novelizations, children's adaptations, and the like.
The least prominent continuity family, this is based around the Go-Bots toyline, encompassing the Playskool Transformers lines and cartoons aimed at ages five and below. (Sometimes called Go-Go-Go-Bots by fans.)
Categorizing stories into their continuity families is a subjective business, so all of the above should be taken merely as operational definitions agreed upon by the editors of Teletraan I: The Transformers Wiki to make our job easier. Therefore, they are not declarations of universal truth.
IDW Publishing's ongoing Generation One comics are clearly beholden to Generation One. Most of the major and minor characters (save the humans) come directly from the Generation One toyline or the Transformers fiction contemporary with it, though some feel this continuity is notably further out from the center than any other continuity designated as "G1". However, it should be noted that the IDW continuity is somehow in the same universe as Earth-616 from Marvel Comics, which both the US and UK Marvel continuities were offshoots from, so it is much closer to the center than most people would believe, if not the most central of all.
IDW's Evolutions line of comics features explicitly alternate-universe treatments of Transformers characters. E.g., the only existing example, Hearts of Steel, sets the G1 characters in the 19th century, where they transform into locomotives, ironclad ships, etc. As Hearts of Steel broadly resembles G1, it is treated here as part of the G1 family. (Though it is arguably further-out than even the main IDW continuity.) Future releases in the Evolutions line may be judged differently.
Some fans think of the movie as being another "reboot" of Generation One rather than an all-new entity. This is largely because several of the characters are new incarnations of G1 characters, or at least use familiar G1 names. Teletraan I: The Transformers Wiki initially decided to treat the movie as a new family as a matter of practicality: the movie was bound to give us large quantities of new information as well as several sub-continuities based on books and comics. Trying to force all of that additional info into already-long Generation One articles would be difficult. Additionally, burying movie-related information in gigantic pre-existing articles would be a disservice to people who come to the wiki looking for information about the movie.
In the end, after more background on the movie became known, it became clear that the movie differed quite a bit from G1 despite a handful of mostly-the-same characters. Also, about half of the robots in the Unicron Trilogy have G1 counterparts (some just in name, others moreso), so there is a precedent for this sort of thing.
The Universe franchise features a meta/cross-continuity family storyline which begins as part of the Generation One/Beast Era continuity family, but also includes characters from the Unicron Trilogy and Robots in Disguise, and even one character from the Go-Bots franchise. However, because the "home base" of the Universe stories is post-Beast Machines Cybertron, it is generally thought of as belonging to the Generation One family.