I'll try and give you a more complete summary here, and maybe this will help you understand the bigger picture.
The proper term for Chinese "fighting arts" or "warring/combat arts" is "WUSHU". The term "Kungfu" as used to describe the Chinese fighting arts is a misapplication of the term that actually means something like "to develop a high level of skill thru diligent practice and training". So, someone could have good kungfu in their wushu, or in cooking, or baking, or carpentry, or mathematics, or whatever. Here in the West, the term kungfu was misunderstood and misapplied to the Chinese martial arts.
Thru simple use the term has stuck however, and most people understand that you mean fighting arts, when you say kungfu. In the general public, fewer people understand the term Wushu, so we still often tend to say "kungfu" instead.
OK, now in the 1950s, the Communist govt. in China decided to create a National Sport and Art. They based this on the traditional fighting arts of China, or Wushu. They took elements of the fighting arts and sort of came up with their own methods, which were designed for optimal visual impact as a performance art and competition venue. In short, they emasculated the traditional fighting arts, and traded them for a beautiful, stunning, amazing, demanding and challenging visual display that has little value as an effective or useful fighting method. This is what is known as "Modern Wushu". It is a government-sanctioned performance and competition art and sport, that is based on traditional fighting methods, and has a superficial resemblance to traditional fighting methods, but has lost most or all usefulness as such. Modern Wushu is an impressive art in its own way. It is very demanding on a physical level, and the top competitors are tremendous athletes. However, they are not true martial artists, if all they have ever trained is Modern Wushu.
I'll deviate a bit here and state that in the earlier days of Modern Wushu, there was probably more useful fighting material that remained in the art, but over the decades it has drifted further and further from the orginal fighting arts, and closer and closer to a gymnastics floor routine. So some people who trained Modern Wushu in the early days may still have an understanding of combat. That is more unlikely in those who studied Modern Wushu more recently.
Taiji also has been included in Modern Wushu. Modern Wushu has its own version of the traditional taiji methods, and these also are done with an eye for performance and competition, at the expense of being a viable fighting tradition in the way that original/traditional taiji methods can still be. My sifu commented to me that he was at a competition where the competitors were performing their Modern Wushu taiji, and he was standing next to Madame Sun, the daughter of Sun Lu-Tang, founder of Sun Style taiji. Madame Sun turned to my sifu and said very cynically, "after years of training and teaching, and now we are reduced to this..."
So at any rate, nowadays when someone simply says "wushu", most people assume they are referring to Modern Wushu. However, the term can properly be used to describe the traditional fighting arts as well. My sifu likes to say "Traditional Wushu" to differentiate from "Modern Wushu".
So when Xue asks, what do you want from wushu? I think he means, are you interested in a performance/competition art, or are you interested in a traditional fighting method, or are you simply interested in exercise and health?
Taiji can be any of these, even all of these simultaneously, depending on how it is being taught, and depending on the background and knowledge of the teacher.
Hope this helps.
