Question about size differences between RC lithum 123a vs non RC lithum123a's

I have TWO lights I need to power, one is a micro Aim sports Pistol Light(150lm)that my .45 ACP wears the other is a combo tactical vertical handle and flashlight for my Beretta CX4 Storm, same caliber. My Pistol light takes one 123a's but they are short and very thin. The vertical grip came with two 123's also Non-rechargeable which are MUCH thicker and longer, I had the pistol light longer so I ordered a kit with some Rechargeable 123a's to back it up, they didn't fit, but they fit my new Vertical combo grip, just as fine, What Gives? What is the real 123a? Why the HUGE difference in size?