Understanding Hellman's TMTO
This is a complex topic. Hence my suggestion:

There is a reasonable tutorial here. Forget the example table above and whatever you are reading and read the tutorial first. The example above is full of vague words and undefined terms. There is a lot going on in the TMTO and things have to be fully defined. 

Even Hellman's paper while  very technical is more enlightening than what you have given above, but the tutorial is more gentle.

In the case keylength is not equal to blocklength, a projection map is used from 64 bits (say) to 56 bits (say) by taking the first 56 bits of the output, since the only goal of the update function along the trails is to give you a pseudorandom walk among possible key values. 

Table vs list, these are valid programming and data management distinctions and the author was sloppy. While they have impact on the exact complexity, they have small impact on the overall big-oh complexity of the attack.