For much of the spring, the reporters who cover Apple (AAPL) have been arguing among themselves about what to call the new iPhone they expect the company to introduce in September.

Some call it the iPhone 5, to match the iOS 5 operating system Apple unveiled to developers three weeks ago.

Some, anticipating that the new device will be a sped-up iPhone 4 rather than a major re-design, have been calling it the iPhone 4S, echoing the nomenclature Apple used two years ago when it introduced the iPhone 3GS.

In a note issued early Monday, Deutsche Bank’s Chris Whitmore is telling clients to expect both — an iPhone 5 and an iPhone 4S.

“With Nokia and RIMM struggling,” he writes, “the time is right for Apple to aggressively penetrate the mid range smart-phone market (i.e. $300-500 category) to dramatically expand its [total addressable market] and market share.”

As Whitmore sees it, an iPhone 4S that is unlocked, priced around $349, and comes with a pre-paid voice plan would “drive significantly greater penetration” into an addressable market that has grown to include 1.5 billion potential customers in 98 countries, two thirds of whom prefer pre-paid plans.

In the U.S., most cellphones are subsidized by carriers with contracts that allow them to recoup the cost of the phone in monthly payments. But as the above chart shows, there are large swaths of the world — especially in Africa, Asia and Latin America, where iPhone penetration is low — where customers prefer to pay the full cost of the phone upfront.

Note that analysts for some time have been calling for Apple to release a lower cost, pre-paid iPhone, and that Whitmore does not cite any sources or claim any inside knowledge for his two-iPhone theory.

[The Loop‘s Jim Dalrymple, however, recalls that COO Tim Cook told Bernstein’s Toni Sacconaghi earlier this year that Apple “understood price is big factor in the prepaid market,” and though the pre-paid market may seem out of Apple’s realm, Cook said that the company was “not ceding any market.”]

In a separate note issued Sunday, Morgan Stanley’s Katy Huberty, back from a week of meetings in Taiwan, reports that she expects iPhone and iPad production to “begin ramping up aggressively” from August through the end of the year.

If production for what Huberty sees as one new iPhone doesn’t start until in mid to late August, the launch might not come until late September. In her unit sales spreadsheet, copied below, she’s shifted 2 million iPhones from calendar Q3 to calendar Q4 (Apple’s fiscal Q4 and Q1 2012). If the launch comes in early September, she says, she’ll shift them back.