A non-provisional application can claim priority to multiple provisional (or indeed nonprovisional) applications. Per 37 CFR 1.78(a):
An applicant in a nonprovisional application … may claim the benefit of one or more prior-filed provisional applications
However, the nonprovisional application (and any Conventional applications filed in other countries) must be filed within 12 months of the earliest provisional application.
Each claim has its own priority date. This is the filing date of the earliest provisional application which disclosed the contents of the claim.
What does refiling mean?
Refiling typically involves two steps: actively abandoning the original application and then filing a new application with the same content.
Thus you are correct, when you say "if the [second provisional application]'s content is different [from the first provisional application's content] then it is not a refiling, but instead the content of the [first provisional application] retains its own priority date".
It is important to note that you cannot just refile without (or before) actively abandoning the earlier one. This is because otherwise the deadline for Convention applications will stay at 12 months from the first provisional, which means the refiling is almost certainly pointless.
Wouldn't it make more sense to do multiple provisional applications in piecemeal fashion so as to claim the earliest date possible for each feature as it is fleshed out?
The catch is that the deadline for filing a nonprovisional or Convention application is set at 12 months from the earliest provisional. If the multiple provisional applications stretch out over more than a year, you're going to have trouble.
The main reason to refile a provisional application is because you want to delay when you file the nonprovisional and Conventional applications. This will typically come down to money (because filing is expensive) and term (because the 20 year term of the patent begins when the nonprovisional is filed).
For example, let's say you filed a provisional application on 1 January 2015. This means the deadline for filing a nonprovisional or a foreign filing is 1 January 2016. However, on 31 September 2015, you realise that you're not going to have enough money to pay for the nonprovisional or the foreign filing. So you abandon the original nonprovisional, and refile it with the same content as on 1 October 2015. This moves the deadline for filing a nonprovisional and Convention to 1 October 2016. Of course, there is the risk that there has been a disclosure in the meantime, so should not be done without due consideration.