Technically the Saturday evening Mass is not a vigil Mass. A vigil Mass is a separate liturgy that anticipates the feast day itself. The Saturday evening Mass **is **the Sunday Mass on Saturday evening.
The origins of the practice go back to the Jewish practice of beginning the celebration of the Sabbath or holy day at sun down the evening before the day.
And, yes, the Sunday Mass on Saturday evening does exist throughout the world. The Code of Canon Law which is the universal law of the Latin Church explicitly states that Mass the evening before satisfies the Sunday obligation (canon 1248 §1).
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