I always thought that "Vajra Posture" and "Lotus Posture" were simply two names for the same thing. But recently somebody told me that Vajra Posture is for males and Lotus Posture for females, though without explaining any physical difference.
Searching turns up mostly interchangeable usage, and a few instances that confirm the male/female difference, though without explanation -- for example https://goo.gl/fxIi2Y and https://goo.gl/U0KKb1
Anybody know the story? Is there a male vs female difference? If so, is it the same physical posture, differing only in the gender of the practitioner, or is there an actual physical difference? Does it vary by tradition? (I suspect the difference is mainly found in the Tibetan / Vajrayana tradition, where the vajra symbolizes a male genital organ and the lotus a female organ.)
Addendum 8/30/2015. I wonder if what's called "half lotus position" in yoga is lotus position in Buddhism. In other words, in Buddhism vajra position is both feet up on opposite thighs, lotus position is just one foot up with the other on the mat. Evidence for this comes from this web site -- http://www.himalayanart.org/pages/glossary.cfm -- which is associated with the Rubin Museum (http://rubinmuseum.org/) -- this entry:
Asana (Skt.): seated or standing postures of which there are a variety of prescribed forms arising from iconographic descriptions found in religious texts. The names of the postures differ between religious traditions. For example the lotus posture in Hatha Yoga is called vajra posture in Buddhism. The half yoga posture in Hatha Yoga is called the lotus posture in Buddhism.
A problem here is that the term "half yoga posture" is not a standard yoga term (according to a web search). But perhaps they meant "half lotus".
Here, by the way, is a site showing both, using the names from yoga: lotus and half-lotus -- http://www.wildmind.org/posture/lotus.
If my conjecture is correct, these are what's known in Buddhsim as vajra and lotus position respectively. Even if this is correct, however, it does not address the gender connection. Maybe that is just a Vajrayana (Tantric) convention -- male figures use the vajra position and female figures the lotus position. But even if so, I'm sure there is a story behind it.