As far as I know it's the same thing. They're just using different terms. Chrome is the name of the browser and you're running the Android operating system on your Nexus 7 so of course it refers to it as 'Chrome for Android'.
As far as flash is concerned...Chrome, like many of the newer browsers is focused on html5 which is the new web standard for video so they don't support Flash. But, if you need or want flash to watch certain videos on the internet that are still using it (and there are many) then it is possible to install Flash on your Nexus 7 but it requires you to do what is called 'sideloading' it. You might then also want to install another browser that supports flash...like an older version of Dolphin or FireFox so you can watch flash videos or play flash games.
I won't go into the details of doing that now...as it exists elsewhere on the forum and it might not be important to you. In a nutshell what you should know is that the entire internet is moving towards HTML5 compliance for their videos which is why all the newest versions of the browsers like Chrome support it. They are trying to hasten the change over to html5 from flash because many believe that flash is an older/battery wasting/bug prone technology and html5 is more streamlined and more stable. As time goes on more and more video on the web will be html5 and less and less flash. Right now since it seems you're a bit new to Android I wouldn't be too concerned with all that. Chrome should be fine for most of your web browsing uses so go ahead and use it.