I'd say neither. In poker (five cards) it's called a "straight" and if all the cards are the same suit: a "straight flush". "I have a straight (10,J,Q,K,A), ace high." I'd use "run" otherwise. Queen, king, ace: three card run.
Considering your text is about poker you should keep "straight". A straight is 5 cards and no less in "normal" poker. I gave you an example above using a straight with ace high. Imagine you have: the 6 7 8 9 and 10. You'd say "(I have a) straight 10 high." Other expressions (while I'm on the subject): a pair, three of a kind, two pairs, a flush, a straight, a full house, four of a kind, a straight flush and a royal flush.
Unless it's been changed, Hela's text doesn't mention poker.
Hela, a "run" is any series of cards in sequence. It depends on the game you're playing as to how many cards you need in sequence to win a hand or a trick (or whatever). However, any sequential group of cards is called a "run" in all card games.
And if you don't have a run, you would say "I don't have a run" or "I don't have any runs" (again, it depends on the game).
And, no, a "full house" is not four aces. If you Google "how to play poker" (or some such), you will find the explanations.
Haven't managed to get my hands (gone into hiding) on my Hoyle's book of cardgame rules, so I'm going from memory. Some people play poker for pennies (dimes with inflation) and can change the rules before each deal thus calling a "four card straight" as being valid for that hand. But "run(s)" is/are the common term. In cribbage "three or four in a row" give a point per card in the run. Hope this helps.