This is a confusion about basic English, which has nothing to do with role-playing games specifically. The basic English (and confusion thereof) translates directly to the usage of the words in role-playing games.
A rule is a specific instruction, meant to be obeyed.
A statement that tells you what is or is not allowed in a particular game, situation, etc.
A ruling is a one-time judgement that's typically based on rules.
An official decision made by a judge, referee, etc.
A house rule is a specific type of rule. It is not any type of ruling.
A rule (as in a game) that applies only among a certain group or in a certain place.
A ruling can certainly lead to a house rule, but they're different types of things.
Scenario 1: For example, we're playing a fast-paced game, and the DM isn't really familiar with grapple rules. The party's monk decides to forcibly take a potion from an ogre in the middle of combat. The player notes that he has multiple feats, skills, whatever related to grappling because his monk is an unarmed fighter, and that he's trying to be dexterous about it. The DM says, "Ok, dexterity plus whatever bonuses on your sheet versus the ogre's strength." then moves on with the fight. That's a ruling.
Scenario 2a: Later, the DM looks up the official grappling rules and finds out the earlier ruling has no relationship to the proper grappling rules. At this point, he studies the official rules and learns how they work. Now, any time the monk wants to grapple, they use the official rules. No house rule has been created.
Scenario 2b: Later, the DM looks up the grappling rules and decides they suck. He decides to assign specific grapple bonuses to each of the monk's feats and skills (maybe the same bonuses he used in his ruling earlier, or maybe not), then uses his simplified version of the rules any time a grapple event happens. In this case, a house rule has been created based on the earlier ruling.
Scenario 3: The DM is starting a new quest chain. He starts looking up stats on various elemental monsters. He discovers that certain elementals have a particular weakness that would allow the party's mage to destroy all of them in like two rounds. So he decides that, for any adventure chain where elementals are a primary bad guy, elementals don't have this weakness. Here, we have a house rule, but no corresponding ruling.
Scenario 4: The party's fighter wants to dual wield a throwing dagger and a short sword. In the middle of the fight, he decides to throw the dagger at a goblin across the room, while still having his short sword active. The official rules make it difficult to decide whether he is a "ranged" character, or a "melee" character, so the group isn't sure whether he provokes attacks of opportunity or whatever. The DM rules (makes a ruling) that the main-hand weapon determines ranged vs. melee, so the fighter behaves as normal, and states that the rule is permanent1 unless it becomes a problem. Here, we have a ruling and a new house rule at the same time, but it is the permanency of the ruling that creates a house rule, not the ruling itself.
Despite the difference between the terms, there is some overlap. In general, if the DM makes a ruling about specific things, whether it's a translation of the official rules, or a made-up idea on how to handle a situation, there is some expectation that the ruling has created a house rule. The longer the DM continues to make the same ruling under similar circumstances, the stronger the de facto house rule becomes. But you generally wouldn't say it's a house rule unless the DM either says so, or it's a regularly recurring ruling.
Similarly, you could narrow the concept of "certain group or certain place" to a very specific idea of "certain", and say that a ruling always creates a one-time house rule for the certain place of "right here, right now".
Additionally, you'll sometimes hear the idea that a ruling made mid-session automatically creates a house rule for the duration of the session.2
But again, that's not the way the word is typically used. Normally, "house" rules, are talking about rules that extend over an entire campaign, or any game run by a particular DM. As in, "when we're at his house, goblins are immune to metal-eating-acid". Not, "that one time at his house, goblins were immune to metal-eating-acid".
As related to D&D 5e
But in 5e, I've encountered people saying that everything from a simple yes/no answer to a question, up to representing the damage of falling ship spars with the rock fall trap are all house rules! Is this just people used to more strict rules systems having difficulty understanding the concept of a DM ruling?
Well, it's both. If your DM specifically decides that for this and future sessions with this ruleset / party / whatever, the answer to the question is "yes", it's a ruling and a house rule3. If your DM decides that this time only, the answer is "yes", it's just a ruling.
But houserules are generally a replacement or extension of the core rules, not just an interpretation of what to do in a given situation.
An interpretation of what to do in a given situation is an extension of the core rules. The distinction between terms is whether we're talking about a one-time decision (a ruling), or a permanent extension (a house rule).
I don't have a full copy of the real DMG (just the free PDF that doesn't talk about DM-ing at all). But from what I could find in a borrowed copy, the book uses the terms "rule" and "ruling" just as I've described above.
To referee the rules, you need to know them. You don't have to memorize this book or the Player's Handbook, but you should have a clear idea of their contents so that, when a situation requires a ruling, you know where to find the reference.
Notice how the rules are something that you refer to when making your ruling in a specific situation.
I can't find anything about "house rules" (though I didn't search the entire book in pain-staking detail), so unless there's evidence to the contrary, I would say there's no official definition of the term that's contrary to the standard definition.
1Of course, "permanent" is somewhat imprecise. The rule can be changed in the future, but is valid so long as it hasn't been changed. And it's not expected to change often, if ever.
2A better way to describe this: there's a house rule that says "mid-session rulings are considered canon for the duration of the session (or until a reasonably-long break)".
3There is an interesting philosophical question here about whether it was actually a "house rule" if it turns out the ruling actually matches a more careful examination of the official rules. But that's probably beyond the scope of this question.