When your device connects with a WiFi Access Point, they identify each other. The AP authenticates that the device knows the password and then they negotiate (handshake) cryptographic keys to encrypt further messages and protect them. PTK and GTK are two such crypto keys. The former is used for direct communication from the device to the AP (normal internet requests), while the later is for something called multicast, which I don’t know for sure but I guess it’s for intranet comunication (between peers in the same network.)
TKIP and CCMP are two different ways of negotiating crypto keys. TKIP (later named WPA) was designed as a contingency measure when WEP security was broken, and was later superseeded by CCMP (WPA2). It was deprecated in 2012, so it’s an obsolete prococol, which doesn’t sounds good at all.
Home ISP routers are bad at security, specially wireless-wise. They are hardly updated, if ever. I have an OpenWRT wifi router linked by an ethernet cable to my ISP router with wireless disabled because it’s a mess.
[I already knew some little things about how WiFi worked (what the handshake was used for), but that was more specific knowledge. It was easy to find at the Wikipedia page you linked.]