The device you are looking for is a Wireless Access Point. It usually has one more more antenna's (which may be internal) and one or more wired network connector.
These devices are getting rarer though. Most of the time people want a modem, a routes and a wireless access point. It is cheaper to build a single device which can do all three functions than to build three separate devices.
Still, as long as you can turn off unneeded functionality even such a complex device will do. Your wireless extenders might actually be quite close to the desired functionality. As long as they allow the right settings they will work fine as a W.A.P. Just connect one port to the regular wired access point (which you described as ethernet plates) and configure it properly. (e.g. no DHCP on these. If using 2.4GH then preferable on different bands then the wireless in the cellar etc.)
If you have a device with antenna's then look at the diagram below. You see that I drew the wireless signal as orthogonal to the antennas. Orientating these in the right way might help a lot to get a better connection on different floors (at the cost of signal strength on the floor the device is on).
