Wiki is not all accurate
There is a difference of Tai Ji and Tai Ji Quan
And Jian is a sword long before TaiJi using it
And Chinese "fencing", is not like European "fencing"
You cant label both as fencing when one is truly fencing and the other is JianShu
Jian Shu, Chinese "Sword Method", is not at all associated with the flowery and degraded "Tai Ji Sword displays
You are the one who initially cited/quoted wiki!
However, I now understand that you are basing your argument on the difference between Tai Ji and Tai Ji Quan (assuming the initial use in the OP and the advert recognised the difference as well).
OK, I understand your point as this: TJ is a aesthetic and degraded style based on original TJQ, utilising visual and auditory effects over practical useage. As such the swrods cannot be considered TJ swords because they are of a different quality/standard/type.
TJQ is a more practical style, utilising sword systems of a more practical nature, as well as utilising swords which were originally used in other styles, therefore are not wholly TJQ swords. As such, it is a misnomer to refer to them as TJ or TJQ swords.
Am I correct?
As for the "fencing" point, of course there are stylistic differences between Western and Chinese sword styles. However, not being familiar with the Chinese term(s) for opponent based combat swordplay, I chose to use a generic Western term.
My use of the term "fencing" is similar to the use of western terminology when describing Chinese swords as "sabres" etc (which would qualify it as "fencing"), or using the term "boxing", when referring to Chinese Boxing. I see no problem using the term "fencing" to mean swordplay against an opponent, especially when it is clear from the context that I do not refer to the different styles of western fencing.
So, does Jian-shu use combat/opponent-based sword-sparring? Also, is Jian-shu the same across different aspects of Wu Shu disciplines?