Does a six pack mean I have a strong core?

No, absolutely not. Your  abdominal muscles (rectus abdominis) known as a six pack is just one muscle group out of many in your core.  Two groups of muscles lie in the core, the outer or superficial muscles and the inner deep core muscles. There are about 20 other muscles in your core that you need to focus on to build a strong core and most of these muscles are deep within and you can’t see.