A gem, or jewel, is a cut and polished precious or semi-precious stone that can be used to make jewelry.
A gem can also be used to describe something that stands out as being better than everything around it, as in "this figurine is the gem of her collection".
A stem is the part of the plant that holds up the leaves and flowers. Stems on some kinds of plant continue to get bigger and bigger, and eventually turn into branches.
Another word for stem is stalk.