The gray one only seems to have two contacts, so it for phones/modems. The yellow one is more common for networking. For compatibility reasons often used in outlets too. The yellow one is RJ45, the gray one RJ11

So, what you are looking for is an RJ45/RJ11 cable. (cat-3 cable will suffice but higher works too). Alternatively you can use an RJ45/RJ12 (same specs). The difference is RJ12 has 6 wires where RJ11 has only two. Since you have only two in the gray one, both can do the job.