Vajra Posture vs Lotus Posture -- the same or male vs female?
There is both no gender difference in the Lotus Posture and Vajra Posture or any other difference whatsoever as far as I'm aware. These are interchangeable terms for the same posture - the former has its root in Hatha Yoga and latter in Tibetan Vajrayana. There is, however, a gender difference in the Sattva Posture which is often recommended in Tibetan traditions if full lotus is not possible. This is maybe where the misunderstanding may have started? In the  'The Tibetan Yoga of Breath: Breathing Practices for Healing the Body and Cultivating Wisdom':


  Sattva posture is done differently for males and females, but both can begin by sitting cross-legged on the floor. Elevating the hips so that they rest above the knees makes the posture easier to hold, so we need to sit on a pillow or cushion. For males, the left leg is tucked in closer to the body and the left foot placed on the inner right thigh, while the right leg rests in the front. For females it is the opposite: the left leg rests in the front and the right leg is tucked, with the right foot resting on the inner left thigh. This posture is similar to a half lotus posture, except that one leg rests in front of the body for balance.