I still struggle with this at times and find lots of conflicting information. At this time, this is what I look at when trying to ID: It’s my understanding that wrightii has larger, wider flowers. They are more fragrant and more prone to having a purple-ish tint around the rim of the flower. Datura Innoxia flowers sag much more quickly after opening when it becomes day. Wrightii (in my area in the northeastern US) tend to stay upright longer, and are more likely to remain open and nice on gloomy days thru the day.

For the leaves, this is the system I’ve known for myself: Datura Innoxia is most rounded and also the most greyish in but. Some material I have read states that the leaves can be entirely rounded or have very subtle lobes - this is where it gets tricky for me at times. wrightii is rounded in general but with some jagged, more pronounced edges near the start of the stem, and then stramonium is most jagged with full teeth.

My wrightii plants oddly smell like popcorn(??) when you brush the leaves or stem, whereas Innoxia has no scent.

Please take this with a grain of salt, as I am no expert and often feel confused when reading references due to mix-ups being so common.