leiotrichous is the word for having smooth hair - from the Greek leios: smooth, plus trikhos: hair.
lissotrichous is having straight hair - from the Greek lissos, which, in addition to straight, also means smooth, thus the confusion.
The terms are rare, but still to be found in the vocabulary of some specialists, especially zoologists.
That these terms exist at all is due to the French naturalist Baron Jean Baptise Genevieve Marcellin Bory de Saint-Vincent, who travelled the world at the beginning of the nineteenth century studying plants. He also made a stab at classifying peoples into races. He is now hardly remembered, but in a once-influential book Homo: essai zoologique sur le genre humain, published in Paris in 1827, he attempted to classify humans with straight and wavy hair into the Leiotrichi and those with woolly or tufted hair into the Ulotrichi, with many sub-groups below these headings.
His classification was seriously studied for several decades, being quoted—for example—by both Thomas Henry Huxley and Charles Darwin.
This little research project has been brought to you by a woman who is not anxious to get to work . . .