According to Canada Revenue Agency, if you are self-employed, you have a business.
If you have a business by yourself, you have a sole proprietorship.
If you have a business with a partner, you have a partnership.
On the other hand, if you choose to carry on a business under a name other than your own personal name, you must register with the Corporate Registry.
Therefore if you operate with your own name, there is no difference.
If you operate with a name other than your own name, you must register.
If you need detailed information please visit to CRA web-site:
http://www.cra-arc.gc.ca/tx/bsnss/sm/menu-eng.html
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