I'm in the states, and they consider 2 dose to be "fully vaccinated". This is relevant for all laws that mention the requirement is to be "fully vaccinated", and that's 2 dose for Pfizer or Moderna and one for J&J.
It is a fairly ridiculous situation and if you need to travel it's definitely an issue given a lot of countries are moving towards "green pass" type actions where unless you are "fully vaccinated" (with the approved vaccine) life will be very difficult for you.
There really should be a better solution about at least the most common vaccines being cross recognized everywhere and not used to artificially block people from moving (why should AZ manufactured in the UK be treated any differently from AZ manufactured in India)
Canada has approved the J&J vaccine, but it has not distributed any such shots. The first shipment it received came from the troubled production facility that operated off-spec, and the shipment was ultimately rejected (https://www.nytimes.com/2021/06/12/world/canada-jj-vaccine.h...). Canada has only distributed AZ, Pfizer, and Moderna shots.