As Karlshammar said, inside vs. outside refers to where the application is processed, NOT where the person being sponsored is located.
Rather than inside or outside, the two are commonly referred to here as INLAND and OUTLAND.
In order to apply INLAND, the applicant has to be physically present in Canada, preferably for the entire duration of the process. It's mainly intended for people who are already living in Canada under another kind of visa (like a study permit or a work permit). If the applicant leaves Canada while it's being processed (for whatever reason) and then can not return to Canada (for whatever reason, like say they don't get another visa to visit), the application is lost (because they no longer qualify as a family member IN Canada) and the person has to apply again.
It is called INLAND because it's processed inside Canada. The application is sent to Vegreville, where it takes about 6 months for CIC to process it. Then, if everything looks ok, the applicant is given approval in principal and a PR soon follows. But they might not give approval in principal and instead send your file to your local CIC office, where depending on how busy that office is, it shall sit for a while before they get to it. That's how some people get to wait for several years to get their PR via inland application.
While it's being processed, the applicant should maintain their legal status in Canada. The fact that you have an inland application for PR in process doesn't give you any sort of status, so you should take care of that yourself (for example by extending the visitor visa).
With an INLAND application, you also have the option of applying for an open work permit. You send the application with the PR application and if you're given approval on principal, then at the same time you also get the open work permit.
OUTLAND applications are processed outside of Canada. You send your application to Mississauga, where they first process the sponsorship part (takes about a month) and then forward the application to a visa office abroad who finishes the processing. How long that part will take depends on what visa office you are going through and the details of your case. You can see the different processing times here:
http://www.cic.gc.ca/english/information/times/international/05-fc-spouses.asp
Keep in mind that's after the one month taken by Mississauga. And the times on there an approximation. You could be done faster than the posted minimum time (for example my application was done in 2 months by Vienna, though the minimum they had posted at the time was 3 months), but then again it could take more than the posted maximum time. A lot depends on how well you put your application together (if they need to ask for more info, it causes delays) and if an interview is required.
In order to apply OUTLAND, the applicant can be anywhere in the world. For processing, they can choose either the visa office responsible for their country of nationality or the visa office responsible for the country they had been admitted to for at least one year. So for example, if one is from Mexico, but living in Germany with a study visa valid for 3 years, one can choose either Mexico City or Berlin to process their application.
People mistakenly believe that if they're already in Canada, they should apply inland, but that is not the case. In most cases, the outland route is faster and even if you've been in Canada for a long time, outland is still available to you.
There's no open work permit available for outland applications.
If an interview is required with an outland application, it will be held at the visa office that is processing it, so the applicant should be available to travel there. Interviews are more the exception than the rule though and only called when there's issues or doubts about the relationship.
Also, in order to issue the PR visa, the visa office will need the applicant's passport, so you'll at some point have to mail it to them. Most offices will mail it back anywhere you want (including in Canada), but some (like New Delhi) will not, so if you're mailing from abroad, make sure about that first.
That should do for a start
