As far as I can tell, they are more or less nothing alike. Although I've not used Matlab, I use GIS software more or less every day at work (I'd consider myself pretty proficient with Mapinfo/Discover, and getting decent with ArcGIS).
GIS is Geographical Information Systems - it kind of combines geographic data with a multitude of other data types, and allows you to do a lot of cool geographically relevant data analysis. I use it for analysis of geochemical, geological and geophysical data (often simultaneously), as well as a lot of general field-prep type work (planning drilling, finding tracks, determining the locations of environmentally or otherwise sensitive areas relative to planned exploration, that sort of thing) but there's a myriad of other applications in other fields (everything from urban planning and service delivery to agriculture and environmental management to military applications and tonnes more).