I wanted to post this inquiry as I am interested in learning how the Bodhissatva Vows are different than those in the Tibetan Tradition.
First of all, the East Asian tradition has moved back and forth a bit over the centuries between using the Mahayana Brahmajala Sutra and the Yogacara Bodhisattva precepts as their main text (the other usually remaining as the secondary text).
For example, when I was ordained, we used both texts for our class material in preparation for the bodhisattva precepts. If I recall correctly, one Venerable lectured on one text, and another Venerable lectured on the other.
Does EA Buddhism make a distinction between aspiring and engaging bodhicitta?
Nowadays it does, but I don't think that this was used before about a century ago.
It's far more likely to use some sort of ground (bhumi) type system, whether the ten grounds of texts like the Prajnaparamita, or 40 grounds from say the Avatamsaka, or other similar systems. The ideas corresponding to aspiring and engaging can usually be found within these systems.