My advice is to invest the time and exchange your license to avoid unnecessary problems.
There are so many different regulations, state by state, that the chances of falling faul with one of them are high.
There is also the problem that the Police may not know how to deal with Foreign License properly.
There is also another aspect that should not be ...
Out of state speeding tickets certainly follow you home, but countries don't share details - in many cases it'd be too difficult, as your rental car for example might have the ticket, and your rental company sends you a bill but the country charges the rental company.
The most likely risk is that your insurance might ask "have you had a speeding ...
California does not recognize IDPs. This Calif DMV page says:
The State of California does not recognize an International Driving Permit (IDP) as a valid driver license (DL). California does recognize a valid driver license that is issued by a foreign jurisdiction (country, state, territory) of which the license holder is a resident.
The IDP is only ...
You should get an international drivers permit. Basically it's a document that's internationally recognized. I don't know for India, but in Denmark it's issued by the same authorities who issues regular drivers' license. It takes 10-15 minutes to make and cost me around 4-5USD to get.
You are probably better off getting a California license:
Tourists may drive rental cars in California for one year as long as they have a valid driver’s license from their home country. See theDepartment of Motor Vehicles (link is external) for complete details.
This California DMV page says:
Adults Visiting California
Visitors over 18 years old with a valid DL from their home state or country may drive in California without getting a California DL as long as their home state or country DL is valid.
You do not need to apply multiple times.
The original question was if you need an international driving license per trip. This should not be necessary. As noted, there are international conventions for international driving licenses.
Nothing in those conventions says that a license would be limited for a single trip or country. The license is valid until ...
Well, you are driving to British Columbia and from the description, the NJ probationary licence is the equivalent of the BC N(new driver) licence, with almost identical restrictions. Since N drivers are explicitly allowed to drive in the US:
http://drivinginstructorblog.com/l-and-n-restrictions/, you'll be fine.
There are 3 slightly different versions of the International Driving Permit: the 1926 Convention, the 1949 Geneva Convention, and the 1968 Vienna Convention. See https://en.wikipedia.org/wiki/International_Driving_Permit for details. You might find you need to apply for 2 permits. Which one(s) you need is dependant on which convention your destination ...