Does the same spell (or potion) have different effects on different people?

Question

When the Weasley twins try to cross Dumbledore's Age Line to put their names into the Goblet of Fire, they are both thrown out after magically sprouting long white beards. Dumbledore walks in on them at this time.

"I did warn you," said a deep, amused voice, and everyone turned to see Professor Dumbledore coming out of the Great Hall. He surveyed Fred and George, his eyes twinkling. "I suggest you both go up to Madam Pomfrey. She is already tending to Miss Fawcett, of Ravenclaw, and Mr. Summers, of Hufflepuff, both of whom decided to age themselves up a little too. Though I must say, neither of their beards is anything like as fine as yours." (emphasis my own)

_{Harry Potter and the Goblet of Fire, Chapter 16: The Goblet of Fire}

Dumbledore says that Fawcett and Summers haven't sprouted beards "anything like as fine as" the Weasley twins' beards.

Does that mean spells (and/or potions) affect different people differently?

I am aware Dumbledore might have just said that for comedic effect. But in the real world (out-of-universe), we know some people react differently to certain medicines, foods, etc. The reasons for this can be allergies or metabolism or something else (I'm not a medical practitioner by any stretch of the imagination so my knowledge on this is basically zero). But the cliché that every human is physically and mentally unique applies here. Does that even translate to magic folk? Can wizards be allergic to certain potions or maybe react differently to certain potions or spells?

Answer 1

Yep.

To add to the fine examples Jonah provided, I'd bring up the Imperius curse. Harry fights this curse (in the example below and again when Voldemort uses it later in the book) whereas his classmates are unable to do so.

Not one of them seemed to be able to fight the curse off, and each of them recovered only when Moody had removed it.
...
"Look at that, you lot! Potter fought! He fought it and he damn near beat it!"
_{(Goblet of Fire, Chapter 15, Beauxbatons and Durmstrang)}

There are three more dubious examples, which may or may not count depending on the scope of the question.

Ron is particularly affected by a Cheering Charm. Whilst this is an instance of a spell having an disproportionately adverse effect the implication is that this was down to Harry's casting rather than any natural proclivity towards cheerfulness on Ron's part. He may be more readily affected by this spell compared to other people - or he may not. It isn't made clear in the excerpt.

Hermione had been right; Professor Flitwick did indeed test them on Cheering Charms. Harry slightly overdid his out of nerves and Ron, who was partnering him, ended up in fits of hysterical laughter and had to be led away to a quiet room for an hour before he was ready to perform the Charm himself.
_{(Prisoner of Azkaban, Chapter 16, Professor Trelawney's Prediction)}

I'm aware that the question was looking for potions or spells but it seems relevant to mention Dementors here as well. Harry faints in their presence whereas others don't.

"The Dementors affect you worse than the others because there are horrors in your past that the others don't have."
_{(Prisoner of Azkaban, Chapter 10, The Marauder's Map)}

Similarly, another creature that affects each person in different ways is the Boggart. No two wizards see the Boggart take the same form so clearly it affects people in different ways.

Answer 2

Yes, it can

Although Dumbledore may not have been entirely serious within the context of that situation, there is ample evidence of spells and potions having differing effects on different people.

• The Auror Dawlish is particularly susceptible to the Confundus Charm:

  Snape was smiling,

  “My source told me that there are plans to lay a false trail; this must be it. No doubt a Confundus Charm has been placed upon Dawlish. It would not be the first time; he is known to be susceptible.”

  —Harry Potter and the Deathly Hallows

• Amortentia, the most powerful love potion in existence, smells different to everyone, depending on what attracts them.

  “And the steam rising in characteristic spirals,” said Hermione enthusiastically, “and it’s supposed to smell differently to each of us, according to what attracts us, and I can smell freshly mown grass and new parchment and —”

  —Harry Potter and the Half-Blood Prince

  Harry smells something rather different:

  They chose the one nearest a gold-colored cauldron that was emitting one of the most seductive scents Harry had ever inhaled: Somehow it reminded him simultaneously of treacle tart, the woody smell of a broomstick handle, and something flowery he thought he might have smelled at the Burrow.

  —Harry Potter and the Half-Blood Prince

• Those of an advanced age are more vulnerable to Stunning Spells

  'She's not here, Potter,' said Madam Pomfrey sadly. 'She was transferred to St Mungo's this morning. Four Stunning Spells straight to the chest at her age? It's a wonder they didn't kill her.'