There are the minimal legal distinctions between naturalized citizens, born-in-Canada citizens, and other citizens-by-birth, as noted by others above, such as that citizens-by-birth not born in Canada do not pass citizenship by birth to children born outside Canada, and while naturalized citizens are not the only ones having citizenship in multiple countries, they are by far the largest group of dual citizens potentially affected by the Bill C-24 provisions expanding grounds for revocation to include certain acts committed after becoming a citizen.
The Charter, however, for example, does not distinguish guaranteed rights relative to the source of citizenship (while, in contrast, the Charter does distinguish mobility rights of Canadians depending on whether they are a Canadian citizen or a Canadian PR). It may warrant noting that Justice Rennie has ruled, in the Galati challenge to Bill C-24, that there is no jus soli right to citizenship in Canada, that all citizenship is based on a statutory grant (thus, for example, that persons born in Canada are citizens by birth derives from statute, not constitutional rights . . . perhaps a precursor to this government further amending the Citizenship Act, if it wins this year's federal election, to restrict citizenship by birth to only those born by a parent legally admitted to Canada, addressing the so-called anchor baby concern (in my view a vastly exaggerated concern).
But generally, a citizen's place of birth is identified in the Canadian passport's biographical information, and this information can result in being treated differently when traveling to other countries. (Such as those born in Taiwan traveling to mainland China; those born in Israel traveling to certain ME countries and the converse, those born in certain ME countries traveling to Israel; not sure if the U.S. still distinguishes Canadian citizens based on birth in certain countries, but for a time the U.S. was requiring more security related procedures for some Canadian citizens depending on their place of birth.)
Canadian citizens may request that their place of birth not be displayed in the passport. But passport Canada posts the following caution about choosing to not display place of birth:
You may request that your place of birth does not appear in the passport. However, if you chose to do so, note that:
-- Place of birth is mandatory for entry to some countries. You should contact the consulate or embassy of every country you plan to visit to ensure that you will be allowed entry if your passport does not indicate your place of birth.
-- You may have difficulty obtaining a visa.
-- You may experience delays at border crossings.
