The Old English word used was binn(e), which is the direct ancestor of our word, "bin." This is a good equivalent of the word we're used to seeing, "manger," though "manger" comes from later French. In either case, we're talking about a solid feed trough. Of course, after the Norman Conquest, literary Old English died out, and nobody looked at the Anglo-Saxon translations again until early modern times.
John Wycliffe, in the 1300's, uses the word cratche. We're used to seeing this word in its French form, creche, referring to a nativity scene. The outdoor nativity scene was invented by St. Francis of Assisi around 1200. So the word -- and the scene -- would be current by Wycliffe's time. Please note that a cratch (later English spelling) is not a solid trough, but a wooden rack for holding hay.
Either object -- a feed trough or a feed rack -- would do, but what in fact is this thing? Latin praesepium, which both English translations ultimately derive from, could mean several things, including "brothel" and "home turf." Leaving aside those improbable translations, the meaning we're thinking of would be "crib, manger, stall." That doesn't seem to resolve the issue, though; in fact, it expands it. So what was the original Greek that Jerome translated into Latin?
In the Greek NT, the word is phatne, and it can mean "manger." But it can also mean "stall." In outdoor contexts, it means "feeding-place." Which means that Luke may actually be saying that the baby was laid in the first floor stall, because there was no room upstairs in the main living quarters (contrasting phatne with kataluma, which refers to the "upper room" of the house). In other words, the infant's bed could have been made up on the floor, as Mary and Joseph's probably was. They may all have been occupying a swept-out stall in the overcrowded house. But, of course, they could also have appropriated whatever was handy for a baby bed.
The animals lodged with the family overnight were probably either donkey(s) or cattle. Both could be fed from either a trough (for grain) or a rack (for fodder). So, you pays your money and you takes your choice.