a module container is a regular container.

Each module can use their own css, specified in the modules CSS file, but you need to make sure that they override any settings in the container.css file or use different CSS classes.

You may want to check out:
Introduction to CSS and inheritance in DotNetNuke skins

module.css is not mentioned in the tutorial as I have seen it placed in various orders, but in most cases you would see it at the beginning or end of the CSS files that are read:

1. module.css
   
2. default.css (Created by DotNetNuke, stored at folder: Portals/_default/)
3. skin.css (Created by your current page skin)
4. container.css (Created by your current page container)
5. portal.css (Created by DotNetNuke for each portal in your installation. A portal.css file template is stored at folder: Portals/_default/ which is copied to each portal folder ie: Portals/0 (each portal number ie. 0,1,2,3) it is this portal.css file that is read by your DotNetNuke skin)
6. module.css

I would then recommend you have a look at: Troubleshooting DotNetNuke Skins which helps for troubleshooting through CSS files and inhertitance problems.