@stef I'm not a native english speaker but I always thought it was another way of saying it and had no difference in meaning.
A quick google search seems to indicate that I'm not wrong, I just prefer twintails because it sounds cuter.
Japan also use twintails instead of pigtails:
Twintails day on 2/2
Ore, Twintail ni Narimasu, a LN about twintails use twintails instead of pigtails
Japan's (dead) twintails association also use twintails instead of pigtails: http://twintail-japan.com/
I'm not telling you to use twintails over pigtails if you don't want to, I'm just rambling a bit.