How to get a full view of the lightning network with c-lightning?
lightning-cli listchannels is what you are looking for to also see the channels and not only the nodes.
In general the lightning nodes learn the network view from the gossip protocol where closed channels may be discarded and not forwarded anymore. If you look proprietary tools like the one you mentioned they might have stored older nodes and channels this is one source how the different numbers can arise.
BTW you get the gossip information from your peers so you could also peer with as many nodes as you learn from your initial peers and hope that you get a larger view of gossip.