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.
97% of NASA staff currently aren't NASA staff. The fucking Centre for Disease Control is on reduced capacity so let's hope the zombie apocalypse doesn't happen any time soon - about half of US Health and Human Serviecs is being sent home. Over 90% of the EPA (environmental protection agency) are gone.
We're talking about several hundred thousand employees sent home without any pay, and even more who won't be sent home and instead will WORK without pay. Air traffic controllers will stay on but have paychecks delayed until this gets sorted out. Same goes for prison guards. The goddamn Federal Court will have to shut down if this lasts more than a couple of weeks. All taxpayer services provided by the IRS are currently out of service.
There are too many groups of people and too many departments and agencies and entities affected to even list.