Hi Nayeem,
Welcome to the community.
Now, you don't really need to know php/mysql to make a class website for a small business. Whether you need to use php/mysql depends on the requirements and aims of the website. You need php/mysql to run a member based web site or to mamange a web site that deals with huge amount of dynamic contents. You don't need php/mysql to build a portfolio web sites.
Now the difference between developer and designer is little abstract. But let's just say a designer mostly works with front end only. A developer is mostly a programmer who deals with the back end. He is the one who writes php/mysql codes. For flash a designer works with the color contrast, theme, and the interface. A flash developer works with action scripts to make it interactive.
Hope that helps.
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