If I get what you are trying to say, you are saying that, you think that the mention of "naturalized" in the Citizenship Clause of the 14th amendment is redundant, because if it omitted mention of "naturalized" (i.e. if it just said "all persons born in the United States..."), there would be no difference since people who are naturalized are, by definition, already citizens, because to naturalize someone means to make them a citizen.
But actually, as later interpreted, including people who were naturalized in the Citizenship Clause does make a legal difference. The difference is that, without it, only a law says they are citizens, but with it, the Constitution says they are citizens. In the decision Afroyim v. Rusk (1967), the Supreme Court ruled that because the citizenship is specified in the Constitution, it is unconstitutional to take away US citizenship from people born or naturalized in the US without their intention to lose it (Afroyim, in particular, was a naturalized US citizen). On the other hand, for US citizens not born or naturalized in the US (e.g. people born abroad, who were US citizens from birth), their citizenship can be taken away involuntarily by Congress, as ruled in Rogers v. Bellei (1971).
At the time of the adoption of the 14th amendment, people who were born in the US were already granted US citizenship by acts of Congress. The reason for adopting the amendment was due to the worry that a future Congress may reverse the decision, for political or racist reasons. If a future Congress would take away citizenship from certain, probably minority, people born in the US, it is conceivable they would also take away citizenship from those minority people not born in the US but who were naturalized. Therefore, if you were worried about it, it made sense to extend the constitutional protection wider, by including naturalized citizens too.