@walk4life This topic comes up from time to time as people try to find the "best calcium" to help ward off osteoporosis.
Coral calcium is simply calcium extracted from broken up coral found on beaches near coral deposits. Chemically it is calcium carbonate - one of the most common calcium supplements. Here is one explanation:
https://www.healthline.com/nutrition/coral-calcium
I don't believe there is any scientific research that shows coral calcium supplements are superior to regular ones.

With two falls and two fractures in a short time, it sounds like you need to think about a slightly different approach - have you had a recent DEXA scan to determine if you have osteopenia or osteoporosis? This would determine whether you need to consider a more aggressive approach to replace calcium lost in your bones vs taking a supplement to prevent bone loss.

Also, you need a PT evaluation of your strength and balance to figure out why the falls. This is nothing to take lightly - the next fall could break your hip - or your head! PT can also give you balance exercises to do at home to maintain or improve your ability to avoid falls in the future.

Let us know what you decide to do...