How to update from JDK8u20 to JDK8u40?

I currently have jdk1.8.0_20 and would like to upgrade to jdk1.8.0_40. Mistakenly, I updated the java to version 1.8.0_40 thinking it would update the jdk too, but it only updated the jre. Does one need to separately download and install the new jdk version and remove the old one or should it update itself automatically or what? I've searched and searched but somehow couldn't find any hint. So either I'm missing something and this is really simple or it's not discussed a lot. Thanks in advance.