The Hebrew word is ‘ger’ and it is not really analogous to ‘natural born’ in American political usage.
The Hebrew word ‘ger’ has two usages, 1) ‘ger toshav’ stranger-sojourner - one who lives in the Land of Israel but isn’t Jewish, instead carefully observing the seven Noahide Laws, and 2) ‘ger tzedek’ - righteous convert to Judaism and full-fledged Jew.
In the verses cited, it is the second use of the word (’convert’) that is used.
There is another word, ‘necher’, that is used for ‘stranger’ but in English is frequently not differentiated from ‘ger’. This would be closer to the term ‘foreigner’.
Thanks jjotto,
Your reply was an interesting read.