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Modular PSUs are also referred to as Full(y) Modular, and semi-modular ones are usually just called Modular. Sometimes you get less cables than your modular PSU can accept, Enermax (for example) love doing this.
Modular PSUs are usually 5-10$ more expensive than their non-modular equals. The difference used to be bigger, but now non-modularity is reserved only for budget/value units. What you as a consumer gain by going for modular is up to you. Some people need/want it as a means of avoiding/lessening cable mess.