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When Harry is in Ollivanders, he holds certain wands and magic happens whilst trying to find a wand match.

Is this similar to when he uses magic uncontrollably in the third book (to inflate Aunt Marge) and what is the spell that happens when Harry Potter first touches his wand?

In the book the 'wand choosing' is simply accompanied by a lack of action until he finds the correct wand.

Harry took the wand and (feeling foolish) waved it around a bit, but Mr Ollivander snatched it out of his hand almost at once.

‘Maple and phoenix feather. Seven inches. Quite whippy. Try –’

Harry tried – but he had hardly raised the wand when it, too, was snatched back by Mr Ollivander.

‘No, no – here, ebony and unicorn hair, eight and a half inches, springy. Go on, go on, try it out.’

Harry tried. And tried. He had no idea what Mr Ollivander was waiting for. The pile of tried wands was mounting higher and higher on the spindly chair, but the more wands Mr Ollivander pulled from the shelves, the happier he seemed to become.

‘Tricky customer, eh? Not to worry, we’ll find the perfect match here somewhere – I wonder, now – yes, why not – unusual combination – holly and phoenix feather, eleven inches, nice and supple.’
Harry took the wand. He felt a sudden warmth in his fingers. He raised the wand above his head, brought it swishing down through the dusty air and a stream of red and gold sparks shot from the end like a firework, throwing dancing spots of light on to the walls. Hagrid whooped and clapped and Mr Ollivander cried, ‘Oh, bravo! Yes, indeed, oh, very good. Well, well, well … how curious … how very curious …’

_{^{Harry Potter and the Philosopher's Stone}}

Harry appears to cast the same spell again in a subsequent book when he's angered.

‘DUDLEY!’ roared Uncle Vernon. ‘I want to know exactly what happened to my son!’

‘FINE!’ yelled Harry, and in his temper, red and gold sparks shot out of the end of his wand, still clutched in his hand. All three Dursleys flinched, looking terrified.

_{^{Harry Potter and the Order of the Phoenix}}

Notably, the appearance of sparks appears to be a common side-effect when a wand is handled and waved. The quantity of sparks appears to be related to how closely aligned the wand is to the practitioner's personality.

Fleur Delacour swept over to Mr Ollivander, and handed him her wand.

‘Hmmm …’ he said.

He twirled the wand between his long fingers like a baton and it emitted a number of pink and gold sparks. Then he held it close to his eyes and examined it carefully.

_{^{Harry Potter and the Goblet of Fire}}

The spell may be related to Relashio which appears to emits hot sparks.

‘Don’ frighten him, now!’ Hagrid shouted, as Ron and Harry used their wands to shoot jets of fiery sparks at the Skrewt, which was advancing menacingly on them, its sting arched, quivering, over its back. ‘Jus’ try an’ slip the rope round his sting, so he won’ hurt any o’ the others!’
...

‘Relashio!’ Harry shouted, except that no sound came out … a large
bubble issued from his mouth, and his wand, instead of sending sparks
at the Grindylows, pelted them with what seemed to be a jet of boiling
water, for where it struck them, angry red patches appeared on their
green skin.

_{^{Harry Potter and the Goblet of Fire}}

or the bog-standard Red Sparks spell (named as 'Vermillious' in the Harry Potter Hogwarts Mystery mobile game). This is a spell that students seem to be able to cast worldlessly even their first year at Hogwarts and which emits a stream of sparks that hang in the air.

‘All right, but I warn yeh, he’s a coward,’ said Hagrid. ‘So me, Harry an’ Hermione’ll go one way an’ Draco, Neville an’ Fang’ll go the other. Now, if any of us finds the unicorn, we’ll send up green sparks, right? Get yer wands out an’ practise now – that’s it – an’ if anyone gets in trouble, send up red sparks, an’ we’ll all come an’ find yeh – so, be careful – let’s go.’

_{^{Harry Potter and the Philosopher's Stone}}