Let me start off by saying that because there is no absolute definition of TIW, nor is there an accepted list of who is or isn't TIW, and because not everyone who even I would consider TIW actually uses that terminology, writing an essay about TIW is likely to be as successful as nailing Jello to a wall. Nonetheless...here goes.
TIW stands for Traditional Initiatory Witchcraft. This label refers to many different paths that often have nothing in common except that they are traditional (but with different traditions), initiatory (but with different initiations and lineages), and practice witchcraft (but in different ways).
The term TIW is a fairly new one, and so it still has not taken root for many people who would qualify under its label. Add to that the complexity that some TIW groups have been around long enough (or not long enough) that they have a name for the tradition they practice at all, so you are more likely to be able to define individual covens, Houses, or groups as TIW moreso than an entire tradition. For the traditions that have been around for quite some time, most of them came out of the 1960s and 1970s mindset where anything practiced magically in the U.S. was termed Wicca. For some of these groups, or for members within some of these groups, they may still use the term Wicca, even though they do not have a lineage going back to Gardner or Sanders.
To make it more complex, some of us do have lineages going back to New Forest--but not to Gardner or Sanders, thus they would be technically Wiccan by some definitions that rely on lineage alone. On the flipside, many TIW groups either started out as traditional Wiccan groups (generally Alexandrian), but they have added so significantly to the core (and, perhaps, deleted from the core, although not being a BTW initiate, members couldn't likely say!), so that they are something else and yet share elements of a common praxis with BTW.
For me, what defines one as TIW, regardless of where they came from or what commonalities they share with Wicca is that a TIW group has taken a different turn in practice and has created something that often blends different traditions and training into a syncretic form of witchcraft.
There is no universal ethical code for TIW practitioners. Some work with the Wiccan Rede, others with various Redes, Tenets and Laws of their line. Most believe strongly in personal responsibility and personal accountability. Likewise, there is no standard deity structure honored across all TIW paths. Many TIW groups may be dedicated to specific deities. Others may not.
Some TIW groups focus on one geographic, cultural, or ethnic form of practice. Others take a more melting pot approach. It is fairly common to see the eight neopagan sabbats and the lunar esbats honored, however the names may vary from tradition to tradition.
In general, TIW practitioners are part of a group, with the exception being those who initiated into a group and, for reasons of logistics, are no longer able to meet with that group, but continue their practices on their own.
To sum up, TIW requires:
Tradition: You must have had a majority of your practices passed down to you from someone else who received them from someone else.
Initiatory: You must be initiated into the aforementioned traditional practice
Witchcraft: You must practice witchcraft, both in your personal day-to-day practices and within a group setting (unless you have had to leave group practice with blessings due to logistics, and even then, you must continue your solitary practices)
In short, TIW is a catch-all name for a lot of non-Wiccan traditions that tend to have a combination of either famtrad, pooched Wiccan lineages, or a few generations (initiatory or genetic) of modern witchcraft practice.
Some examples that I would put under this list (although not all of them would self-identify as TIW at this point) would be groups like Clan of Tubal Cain; different groups within the Alliance of the Old Religion; the Oak, Ash, and Thorn tradition; Assembly of the Sacred Wheel; Keepers of the Ancient Mysteries (KAM); the Roebuck line; some groups within ATC; Blue Star groups that do not want to identify as Wiccan; Feri; NECTW; some Strega lines; and so on.
NOTE: For those who meet the qualifications listed above for TIW but publicly state they do not want to be called TIW, their own individual identification needs trump any classification that I or others do for them in this regard.