GS324TP S350 Switch are SFP modules "fiber only"?

I have a GS324TP S350, it has been working fine for the last 2 years.

I recently acquired a new piece of equipment (a NAS) which has 2 2.5Gb ethernet NICs in it, so I thought, "hey, finally a reason to get a couple SFP modules to install in my switch, which I did, but they did not work.

I am a newb in the world of SFP modules.  I've read the manual for the GS324TP S350 and in several places it says "fiber SFP ports".  My first question is, does it matter whether the SFP module is copper or fiber based?  The modules I bought are copper based. 

I've looked for a list of compatible SFP modules for this switch, and have not found one.  Am I wrong in thinking any SFP module is just like any other?  I'm assuming that is not the case, as when I plugged the two modules I bought in to my switch absolutely nothing happened.  The modules I bought are 2.5/5/10mbps ethernet form factor.

My final question is, is there anything special about those ports once they have working modules installed?  Do they have to be used for connecting two switches together?  Is there any reason a regular LAN client device can't be attached to the switch using one of these ports?  I've seen some documentation which makes it sound like the purpose of those ports is for connecting two switches together, but it is not clear if that is to the exclusion of any other use case.