I agree with everything FordGT90Concept has said. Where does the other end of that CAT3 cable go? Is that from your ISP? If not, then you should replace that CAT3 with at least CAT5e, preferably CAT6 to carry you further into the future. CAT3 was never intended for networking. In fact, it has often been referred to as VG or voice grade cable. CAT5e and CAT6 can, however, be used for telephones.
CAT3 is for telephones and uses RJ-11 connectors.
RJ45 connectors are for "Ethernet" or network cables.
Routers do not use RJ11. Now a DSL "modem" will connect to your ISP via RJ11 but the modem then converts (
modulates/
demodulates) the signal for use with networks. So your side of the modem will use an Ethernet cable to your router.
If you have an integrated "residential gateway" device, the modem and router (and 4-port Ethernet switch and usually a WAP or wireless access point) will be integrated into one box. 4 discrete devices that just happen to share a common case, circuit board, and power supply. But it will still have only Ethernet on your side of the device.
You say this is for fiber. Where is that coming from?
As far as actually answering your question, color coding really does not matter - it is just used to ensure standardization and avoid confusion. All that really matters is the correct data conductor is placed on the right pin. The color coding of the wire that puts it there does not affect that. So you could use a simple
cable tester.