Some browsers are uses the same rendering engine and some are not.
For example:
Google Chrome and Safari browsers are using : Webkit Engine (See: http://www.webkit.org/)
Firefox is using Gecko Engine (A.K.A. Moz) - (See: http://en.wikipedia.org/wiki/Gecko_(software)
Opera is using : Presto (See: http://www.opera.com/docs/specs/productspecs/)
So differences between rendering engines are normal. Which is why we are using their css properties like;
-webkit-border-radius /* For Webkit */
-moz-border-radius /* For Gecko */
-o-border-radius /* For Presto */
border-radius /* For IE9+ */
Some older browsers like Internet Explorer 6, 7, 8 are not giving support for most of CSS3 methods. To enable that methods, there are available to use JS engines like html5shiv or modernizr.
Note: You can use a service like this to generate starter templates that supports almost every browser.
Initializr: http://www.initializr.com/