The distinction is more clear when indexing actual text and applying tokenization. A "typical" index on a database column goes like "column(value => rows)". When people mention inverted indexes its usually in the context of full text search, where "column value" usually goes through tokenization and you build an index for all N tokens of a column "column:(token 1 => rows)", "column:(token 2 => rows)",... "column:(token N => rows)".
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The distinction is more clear when indexing actual text and applying tokenization. A "typical" index on a database column goes like "column(value => rows)". When people mention inverted indexes its usually in the context of full text search, where "column value" usually goes through tokenization and you build an index for all N tokens of a column "column:(token 1 => rows)", "column:(token 2 => rows)",... "column:(token N => rows)".