You have a LTA (M. doreensis). He is an anemone that like to burry his foot in the sand. We call them one of the sand bed anemones. If he doesn't have sand, he will make do with the rock but you need to add about 3 inches of sand to the tank if you want to make him happy.
The small anemone is a S. tapetum, Mini carpet the Maxi variety (there is a mini and micro variety also). he will be fine. He just move if he is shaded by the larger anemone. They my sting each other if they touch.