The distinction, I believe, is that both The Buddha and Muhammed had contemporaneous, official reports about them.
In the Buddha's case, that most definitely isn't correct.
In fact, historians still aren't sure exactly when the Buddha lived. Traditional Sri Lankan accounts place him in the 6th century BCE. More recently, Western historians, basing their arguments on various strands of evidence such as Indian Sanskrit accounts, have placed the Buddha about 100 years later, in the 5th century BCE. And most recently, the exciting archaeological discovery of signs of the existence of a very early identifiably Buddhist structure at the site of the Buddha's parinibbana/death have been dated to the 6th century once again. There's still active controversy among scholars on the subject of the buddha's date and there's a large literature on it.
As far as textual evidence of the Buddha's existence, the earliest extant reference to the Buddha and his Dhamma are found in the emperor Ashoka's pillar edicts dating from the 3rd century BCE (200 to 300 years later). There are no contemporaneous accounts of the Buddha that I know of.
(Both the Buddhists and the Jains agree that representatives of their traditions met and debated during the lifetime of the Buddha, and Western scholarship is inclined to accept that it's true. But in both cases, the writings that purport to record these encounters were written centuries after the events.)
The oldest Buddhist religious writings extant today are found in the Pali canon. These were finally put into writing at about the same time that the Christians' New Testament was written (or perhaps a little earlier) after gradually developing as a very elaborate oral tradition, preserved by the monastics, for something like 500 years previously. What might have motivated finally putting that tradition into physical written form was the appearance of new and doctrinally different Mahayana sutras that seem to have been in written form from the very beginning.
Needless to say, there's all kinds of modern textual scholarship seeking to describe how that oral tradition developed in the early period, often using techniques that were originally created in Biblical Old Testament scholarship. (The OT is another set of writings that developed gradually out of an earlier oral tradition.) Clearly older and newer strands of tradition can be teased out of the Pali Canon. (Everyone agrees that the Vinaya (the monastic rule) was codified comparatively early and that Abhidhamma (an ambitious psycho-philosophical analysis of all possible experience) was a later development.)
A big difference between Buddhism and Christianity is that Buddhism doesn't revolve around the life events of its founder in quite the same way as Christianity does. The Buddha's importance is primarily as the (re)discoverer and expounder of the Dhamma, the Sasana, the Buddhist teaching. The Buddha even said it about himself: whoever sees the Dhamma (teaching) sees me. In other words, however the tradition originated (and it does show abundant evidence of being the elaboration of a single extraordinary vision), the person who originated it (whoever he might historically have been) was the Buddha.
That means that Buddhists aren't typically as interested as Christians in the literal historicity of the traditional stories of their religion's founder's life.
In fact, a whole genre of moral teaching stories developed around the Buddha, called Jatakas, that purport to recount events from the Buddha's previous lives, all with strong Buddhist moral lessons associated with them. Lay Buddhists traditionally grew up with these stories, and they constituted their education in Buddhism, so to speak. (Much of what we associate as Buddhism today, meditation and such, were mostly things for monks.) Modernist Buddhists today give these stories little or no literal historical credence, but they still retain all of their value and charm as teaching stories.
An odd historical aside: Some of these Buddhist teaching tales found their way into Islamic tradition, and even into medieval Europe. A fascinating example is the medieval Christian story of Barlaam and Josaphat ('Josaphat' is derived from 'Bodhisat') which basically tells the story of the Buddha leaving home and eventually finding enlightenment. Josaphat's spiritual quest so impressed the medieval Christians that the Catholic church declared him a saint! The Buddha is a Catholic saint! True fact.
