Your last question is the easiest - yes, there are three teaspoons in a tablespoon. The other part is a bit baffling. We’re assuming the mysterious TBSP 4 TSP is bigger than the tablespoon in your set. There is a British measure called a Measuring Tablespoon, which is three British teaspoons (half again as large as US teaspoons) or 4-1/2 US teaspoons. Even though it appears to be a half-teaspoon short, there is some chance the mystery spoon is a Measuring Tablespoon, intended to help you follow British recipes. But, if so, you might think there would be a British teaspoon in the set, as well.
There was a short piece in Gourmet Magazine a couple years ago about the large variations in capacity between various tablespoons currently on the market, and how imprecise they are. Given the variations the Gourmet staff found, it probably doesn’t matter that much which spoon you use, it may not be very close the actual standard anyway.