How does the Bitcoin network maintain the chains created when two nodes generate different versions of the same block?

How does the Bitcoin network maintain the chains created when two nodes generate different versions of the same block?

I came across these lines from the Bitcoin whitepaper:

If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer.

Does that mean two chains are maintained in parallel in each node? If yes, how do the nodes actually maintain it in implementation level of the Bitcoin network?

http://bit.ly/2T9TaIb