Do you mean to say using any of these two adapters (4 pin/8 pin) on my network makes no difference?
For 10/100, probably no difference. However, the first card (with 4 wired pins) may be an older 10-BaseT card only, especially if the port next to it is coax (which went out of style for ethernet years ago.)
How will I know if my network employs 10/100/1000 BaseT Ethernet?
For one thing, Cat5 cable isn't good enough for Gigabit. So unless you know that you've set up for Gigabit, you don't have it. As for 10/100, most systems these days are "auto-negotiating", which means that 100-BaseT devices are capable of working at 10-BaseT rates if needed (and also at either half or full duplex), to accommodate any older devices on the network. Just make sure your switch or hub isn't 10-BaseT only!
If you're curious, in Windows you can bring up the properties dialog for your network adapter (e.g. Control Panel -> Admin Tools -> Computer Mgmt -> Device Manager -> Your adapter -> right-click): In the Advanced tab, click on "Connection Type". The value shown will probably be "Auto-negotiation" but the drop down will show what else the card is capable of.