Uniformity

What is the difference between "Mozilla/Firefox" and "Internet Explorer?" And why do web-sites, my web-sites, appear differently on them? It's kind of confusing to me that when I have created my web-sites and viewed them upon the different browsers some things appear differently. I'm just wondering if this normal or is it due to something I did or neglected to do back in the creation phase. For instance, I have added for some text to appear when the mouse is dragged over certain pictures on my sites. In I-Ex it shows up, but not on F-fox. But then on F-fox my web design is centered and has the border I made in NvU, while on I-Ex it's off. I don't know, maybe it's a trade off. Hopefully, I'll figure out before too long some of the tricks of the trade.