Um... wtf are you talking about? It's entirely different. All prorogation is is the end of a session of parliament. It has NO EFFECT on the day to day goings on of government and the services government provides. It just means that during the duration your member of parliament isn't reviewing, drafting, and passing laws.
The government shutdown results in the vast majority of government workers no longer getting paid. It is not at all limited to the house no longer going to work. The entire country has no budget and therefore no budget. NASA, for example, shuts down and powers off. All national parks are closed. All government museums are shut down. The essential services run on a skeleton crew.
You have absolutely no clue what you're on about, this has never happened in Canada, certainly not in our lifetimes, because it's an absurd stunt that should never happen.