In
BrE, a "nursery" can be a baby's bedroom, a shortened version of "nursery school", which is for children of between about 2 and 4, or another word for a garden centre (a shop selling plants and other garden equipment).
A "creche" is normally an area in a workplace where people can leave their children at the beginning of the working day and pick them up again at the end. It's not necessarily at their own workplace. There are creches which are in separate buildings. It sometimes applies to a place where children are looked after but not connected to work. For example, at a wedding I attended recently, the bride and groom told everyone that there would be a creche facility available where they could leave their children while they (the parents) came to the wedding and the party afterwards, without having to bring and worry about their kids.