Glad to have cleared it up!
To complicate matters, butterfly and batwing bow ties can both be pointed.
After looking more into batwing bow ties, Drakes calls their pointed butterfly bow tie a "batwing" and calls their straight bow tie a "square end". That's not the usual terminology, but ultimately people call anything whatever they want to.
I think that because Bow Ties are still not quite in the full limelight of fashion, that there is some non-standard terms being used. I have seen a few sources and some internet web pages describing bow ties and they don't always agree. I have also seen, as I posted earlier, Batwing ties shown with a bit of flair but advertised as simply Batwing. I had assumed that they flared a bit like a Bat's Wing, not like a Cricket Bat as you stated, so the confusion only mounted. I have also seen STRAIGHT end bow ties listed just as that, Straight end.
I do like the look of a Butterfly Batwing because of the SLIGHT flair on the end. I think it gives the tie a pleasant look when worn. Of course, you body type and the style YOU prefer makes a difference. I used to live in Paris and I have seen some gentlemen there sport this kind of tie, with a slight flair out on the bow, but not a full butterfly by any means. As I say, if the Bow Tie was as popular as the standard necktie, we'd probably have more standardization in how they are classified.
So this thread has been very educational for me.
Sorry to ramble, but the PRIMARY reason I am a fan of Bow Ties (now) is because of the DISTINGUISHED GENTLEMAN'S RIDE
This is a yearly VINTAGE and CLASSIC motorcycle rally and ride to benefit men's prostate cancer research and men's suicide prevention. I have a very classic 1982 Honda GL-500 Interstate that I ride each year to help raise money for this worthy cause. The THEME of this ride is Classic Vintage Motorcycles and WELL DRESSED Men. You must have both. You can't show up on a 2018 Kawasaki Ninja and wear leathers. We dress in our best and ride our vintage machines. A Bow Tie is perfect for a well dressed man on a vintage motorcycle, as a long necktie in the wind may not be prudent. And the rest, as they say, is history. Now I am a Bow Tie fan!