If this isn't the correct exchange for this question, please let me know. I found a PCIe slot which is described as
1 PCIe Gen3 x4 slot /x16 connector
I'm not sure what they mean by this. Is it simply that the slot has an x4 connection but is open-ended such that it can support an x16 card?
Your assumption is correct. This would be a slot with only four PCIe lanes connected, but it can fit a 16-lane card.
This is pretty common, as PCIe devices are meant to be able to negotiate their connections and use lower bandwidth (usually at the cost of performance) when that's all that's on offer.
This is not always true though - I have seen some graphics cards and one RAID controller in my time that refused to work in anything but their full designation (x8). But I've also seen hundreds of devices that were fine. So your mileage may vary on success.