I started out with the Blue from American Express student version and once my schooling was finished, I got an upgrade to the regular version of the card. The upgrade didn't involve any hard or soft pulls and I kept my same credit card number - it was simply a matter of, "I'm finished with my schooling and would like to continue to use this card. Is there any way to upgrade my account to the regular version of the card or some other similar product?" and the company agreed with me and did the upgrade.
In my case, besides my schooling being finished with, my credit history had also 'matured' more and I was at a level where I could apply for and get approved for a good non-student-version credit card.
Generally speaking, if you maintain a good credit history with the companies, you should be able to upgrade to their 'normal' versions in a similar manner once you're past the 'student' level of the card and have shown responsibility towards credit.
Best of luck!
AMEX: Everyday (MR), Macy's (cobranded)
MASTER: Citibank Dividend Platinum Select (non-World version)
VISA: Chase Amazon Signature, Chase (bank issued)
GE: Care Credit (medical expenses), Macy's (store), JCP (store)
AMEX: Costco True Earnings
VISA: Chase Ink Cash