The moves do not have to be consecutive.
If this position was reach with White to play on move 40, 45 and 55.
White could, before making his 55th move, claim a draw stating the position
was about to be created for the 3rd time.
Officially there is no such thing as a perpetual check (though everyone uses the term)
A perpetual check will produce a three fold repetition of a position when a draw can be claimed.
A player may claim a draw if after 50 moves no pawn move or a capture has been
made during that time. What may not be too well known is if no capture or a pawn
move has been made after 75 moves An arbiter can stop the game and declare it drawn.
This is stop two happy chaps playing on and on and on with neither side
claiming a draw under the 50 move rule.