Heathfield is correct insofar as origin is concerned but nationality is a politico-legal concept. Any new country decides its rules regarding the right to nationality and an independent Scotland will do the same. The UK has rules based on not only where one is born but also the nationality of the parents. Anyone born outside the UK to non-UK citizens has to apply for UK citizenship (if he/she wishes) and then a different set of rules come into play. Anyone with UK citizenship but living outside the UK is a UK expatriate and a non-UK citizen living in the UK is an expatriate from his/her country. A Scottish citizen (after independence) living in the UK (i.e. outside Scotland) will thus be a Scottish expatriate and a UK citizen will be an expatriate in Scotland. How the rules regarding the rights to Scottish citizenship after independence will treat current UK citizens with Scottish connections remains to be seen. Clearly, at a minimum those of them living in and with a history of residing in Scotland will have an automatic right to citizenship - anything less than that would see Scotland starting conceptually with zero nationals. Strictly speaking that will of course be the factual case until the first citizen is registered but the concept will be that the vast majority of residents will automatically become citizens upon independence. What is perhaps the more intriguing question is whether the UK will out of feeling snubbed strip everyone in Scotland of their UK citizenship - I very much doubt it but some of those taking part in discussions on AB about the referendum, etc. may well see that as a natural consequence (the oft mentioned "OK then, be like that", all-or-nothing option.
If Scotland adopts the high passport issue fee rate charged in the UK then the real cost of passports will fall almost entirely onto the applicants. However, if Scotland adopts the non-UK practice of issuing identity cards on demand and enters Schengen then most Scottish citizens will not need a passport unless the UK requires it. Now there is a fascinating prospective example of refusal to be like or accepting any of "them".