Home sick. He misses his home. Nostalgic is different. It means fond wonderful memories brought about by a similar situation. For example- I love Christmas, the tree reminds me of my childhood, i feel nostalgic, thinking of my family all gathered around our Christmas tree, such a good feeling.

I agree that the dictionary definitions are misleading. These two words are NOT used in the same way. Feeling homesick is a personal emotion when you miss your home and family. Nostalgia is a longing for the past, when you look back with fondness at an earlier time.

After looking online, they can apparently mean the same thing, so I'll just tell you my thoughts. "homesickness" (homesick) is a negative feeling you get when you miss your home/family. "nostalgia" (nostalgic) is when you look back fondly on a period of time in the past and may wish to go back to that time to experience it again. For your example, I would use "homesick". If his family weren't alive anymore and it was just his childhood he was missing (looking back fondly on the time he was with his family, for example), I might use "nostalgic".