Tsumasaki-geri is a kick with the tip of the toes. Some would argue that this is the right way to kick (the old way of Okinawan kicking), compared to our ordinary Mae-geri, where we generally kick with Koshi.
Personally, I do not think there is a new or old way of kicking. Nowadays, Mae-geri, were kicking with Koshi, is the preferred way to kick. Most of all, to protect our toes so they do not break. We are simply not trained to kick with the tip of the toes.
Of course, both methods are fully usable, and if you prefer to kick with the toe tips, it might be a good idea to make a small fist with your toes. In that way, you will achieve better stability, and the possibility of broken toes is lesser.
Take a look at the picture from Greek Pankration, which was introduced about 648 BC in the 33rd Olympiad. The use of Koshi.
Good kicking to all