I´m not sure if gemütlich and gezellig means the same. Gesellig (in German) means, that you are together with other people in a pleasant way. Gemütlich has a main definition, but means something different for everyone. First it means something is comfortable for you, you simple like it. For example a warm place with a soft sofo or something like that. If you say someone is gemütlich it can mean, the he is relxed. That´s the positive way. It can also mean, that he is slow or uninterested, that´s the negative way.

If you show people pictures from places and ask if it is gemütlich, you will get very different answers.