A natural run
4♥ 5♥ 6♥ is a pure sequence because the suit is constant and the ranks advance by one. Add 7♥ and the group is still pure. A pure sequence never borrows a joker.
Valid pure sequence
Three hearts, consecutive ranks, no substitute.
One missing card changes the group.
4♥ 5♥ 7♥ is a near miss. The ranks skip 6. It is not a sequence until the missing card, or a joker used under the impure rule, closes the gap.
A run with a substitute
4♥, a joker, and 6♥ can stand as an impure sequence if the joker is allowed to play the 5. Call it impure. Do not count it as the pure sequence your declaration still needs.
Three matching ranks are something else.
8♥ 8♠ 8♦ is a set. The ranks match and the suits differ, so there is no order to follow. A set is useful. It is not a pure sequence.
Keep the whole hand in view.
A beautiful run does not finish the hand. Count to 13, keep one group pure, and place every remaining card in a sequence or a set before you declare.