Differences between 股份有限公司 and 有限公司
The difference is legal. 

有限公司 is a limited liability company (LLC), usually a smaller company.

股份有限公司 is a public limited company/private company limited by shares (PLC), usually larger companies whose shares (股份) are traded on the stock exchange. 

PS. I am not quite sure what are the equivalent of these two forms in your country (Common law, I suppose). In the Roman law based German and Central European law the first would be GmbH, latter would be AG.