Are all the half-bloods treated the same way in the wizarding world?

Question

What is the exact definition of Half-bloods? For example we know all of these cases will be half-bloods:

1. Pureblood + Muggleborn = Halfblood (e.g. Harry Potter)

2. Pureblood + Muggle = Halfblood (e.g. Tom Riddle)

But what about all below cases:

3. Pureblood + Halfblood = Pureblood / Halfblood ? (e.g. Harry and Ginny's son)

4. Halfblood + Halfblood = Pureblood / Halfblood?

5. Halfblood + Muggleborn = Halfblood / Muggleborn. (suppose Snape and Lily's son)

6. Halfblood + Muggle = Halfblood / Muggleborn.

Now in the first 2 cases, we see Harry had both parents as wizard and witch (however muggle-born). However Tom Riddle has a complete muggle for a dad and a witch for a mother. So, is Harry more half-blood than Tom Riddle? Similarly, is case 3 more half blood than case 4 (if both are considered half-blood). Same way, is case 5 more half-blood than case 6 (again, if they are considered half-bloods)?

Answer 1

They're higher-status than Muggleborns but not as high as pure-bloods.

Half-bloods have nowhere near the status that pure-bloods do. Bellatrix tells Harry not to besmirch the Dark Lord's name with his half-blood tongue, calls him a 'filthy half-blood', and is greatly offended and upset on behalf of the Dark Lord when Harry accuses him of being a half-blood as well.

“Yeah,’ said Harry, maintaining his tight grip on the glass ball, expecting another attempt to bewitch it from him. ‘Yeah, I’ve got no problem with saying Vol––’

‘Shut your mouth!’ Bellatrix shrieked. ‘You dare speak his name with your unworthy lips, you dare besmirch it with your halfblood’s tongue, you dare –’

‘Did you know he’s a half-blood too?’ said Harry recklessly. Hermione gave a little moan in his ear. ‘Voldemort? Yeah, his mother was a witch but his dad was a Muggle – or has he been telling you lot he’s pure-blood?’

‘STUPEF––”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 35 (Beyond the Veil)}}

However, half-bloods aren't as badly treated as Muggleborns. A wizard charged with being a Muggleborn by Umbridge's Muggle-born Registration Commission said he was half-blood while pleading his case.

“And then, abruptly and shockingly amid the frozen silence, one of the dungeon doors on the left of the corridor was flung open and screams echoed out of it.

‘No, no, I’m half-blood, I’m half-blood, I tell you! My father was a wizard, he was, look him up, Arkie Alderton, he’s a well-known broomstick designer, look him up, I tell you – get your hands off me, get your hands off –”
_{^{-Harry Potter and the Deathly Hallows, Chapter 13 (The Muggle-born Registration Commission)}}

There don't seem to be degrees of half-blood.

To a pure-blood family, anything less than completely pure is a disgrace. A half-blood is a half-blood, regardless of how pure either of the parents were before. Nymphadora Tonks would be considered just as half-blooded as Tom Riddle, despite the difference between their parents' respective statuses. All four cases in your question would be considered equally half-blooded by wizards who adhere to pure-blood standards.

Answer 2

As always in this case of situation, there is the Purebloods, and there is the others.
As long as you don't marry a Pureblood, your descendence is forever 'tainted' (for whoever cares about it).

Most of the Magical world don't care about Pureblood anymore. Especially when there is proof that even Muggleborn can be very powerful/Intelligent.

But for whoever purist that cares, the son of Harry and Ginny is not a Pure blood, period.

So basically, there is no difference in they way they are treated. Either their blood level is ignored, or considered as 'not pure'.

Answer 3

I guess the easiest way to define this all is to use the parent and grandparent method:

Pretty much everyone considers the pattern of:

• no Muggleborn grandparents or no Muggleborn parents = Pure-blood

Some consider:

• no muggle (only 1 Muggleborn) grandparents, no muggle/born parents = Pure-blood

Therefore, some would consider the new gen to be Pure-bloods, especially since both sides of the family are from before the ISoS. Others would say that the kids would have to marry either Pure-bloods or certain Half-bloods for them to be considered Pure-bloods.

Answer 4

A Muggle-born is someone who has no wizarding lineage.

A Pure-blood is someone who has no Muggle lineage.

A Half-Blood is someone who has both wizarding lineage and Muggle lineage.

Thus in all four of your cases the offspring would be a half-blood.

A few relevant quotes:

Deathly Hallows

“‘Recent research undertaken by the Department of Mysteries reveals that magic can only be passed from person to person when Wizards reproduce. Where no proven Wizarding ancestry exists, therefore, the so- called Muggle-born is likely to have obtained magical power by theft or force.

Ibid

“I know,” said Lupin. “Nevertheless, unless you can prove that you have at least one close Wizarding relative, you are now deemed to have obtained your magical power illegally and must suffer the punishment.”

Half Blood Prince

“The Death Eaters can’t all be pure-blood, there aren’t enough pure-blood wizards left,” said Hermione stubbornly. “I expect most of them are half-bloods pretending to be pure. It’s only Muggle-borns they hate, they’d be quite happy to let you and Ron join up.”