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For example:

Say I plug in two 100-bulb strings in series - one into the other. Each is a series of 50 lights wired in parallel.

Would it then follow that now there are now four strings of 120v, even though only one source of 120v (the wall outlet)?

See this diagram picture I drew illustrating this:

enter image description here

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No - each set of lights still sees 120 volts, and the whole assembly still needs 120 volts.

The 120 volt line and neutral wires from the plug on the first set go directly to the socket on that set. The strings of lights in that set are wired between the line and neutral wires, and do not interfere with the 120 V connection between plug and socket.

As far as the second set is concerned, the first set is just an extension cord.

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