A type of
cryptic crossword which breaks some of the usual rules.
Usually, but not always, these puzzles use heavy bars instead of black squares to separate words on the same line. These bars usually hold to the cryptic crossword convention that there can be unchecked letters, but not two of them in a row in the same word.
What makes them "variety" is that there is often some extra trick, the gimmick of that particular puzzle. Sometimes you have to drop letters out of certain entries (or all of them) in order to fit them into the grid. Other times there may be more unusual gimmicks.
Sometimes the puzzle comes with instructions about the gimmick. Other times you'll be told some entries must be modified to fit them into the grid, but you will have to figure out how the modifications work. When there are modified grid entries, sometimes the word lengths will be withheld in order to hide the changed answers better. However, you'll usually be told if any answers are multiple words, hyphenated, etc., and the instructions may comment on the number of changed grid entries which are proper nouns, multi-word phrases, etc.