Nano basically just uses a block lattice, which looks like a blockchain for each individual user. Blocks are broadcasted across the network and confirmed when you receive the block, and ask the representatives to vote on if the block is legit. Representatives are chosen by users, with the reps having the highest Nano backing being chosen. This gives a network setup where once the block is broadcasted, asking the peer if it's good is the only delay. There is a small PoW on each block, which is to stop blocks from being spammed against the network (however it can be precomputed..)
Disclaimer: built some apps on top of Nano, decently pleasant experience. I keep up a bit with the development of the node software.
NANO uses both a DAG and blockchains. The DAG itself is nothing more of a way to say transactions don't have to wait for blocktimes, they just show up as they happen instead of waiting in line for the network.
In NANO every account is a virtual blockchain. This means when you want to send funds, you have to "mine" a low-difficulty block on your own account and simply publish the results of that block to the network. No one does any real mining in NANO, you can think of "mining" your own blocks the same as signing or encrypting messages. Check out https://nanospeed.live for a speed test.
I'm not related to their team or that website and I don't own NANO, but I do follow their news and liked that site.
Coinmarketcap just reflects what people invest in at a certain time, it doesn't mean that these investments are rational or are based on highly calculated decisions. A lot of coins in the top 100 are copycats, tokens or just concepts, very few are fully functional products.