The Shepherds had a chorus of angels to announce the birth of the Messiah, the Christ
This declaration took them to find Jesus wrapped in swaddling cloths lying in a manger
He Wise Men as far as we know did not have a heavenly host appear to them
They are called Kings, Magi, Wise men it comes from ancient Greek and Chaldea absorbed into Babylonia - Semitic nation – Magi were, practitioners of magic, to include astrology, alchemy and other forms of esoteric knowledge
For them the new star was what announced the Messiah, they probably worked for rather than were kings, but were allowed to set off on this journey.
We don’t know how many – 3 gifts! Nor where they came from apart from ‘eastern lands’
They like so many made the mistake of thinking that Messiah would be born and know to the royalty of His time. Born not in a small village but a royal city.
They obviously did not have the Jewish background history! Nor perhaps the courage of conviction in following the star, over expectation!
We know about their brush with Herod, the Bethlehem link finally following the star to its destination.
Arrive at a house – not stable! Joseph absent – at work probably.
From Herod’s actions they had been travelling for anything up to 2 years! Did the star appear at His birth or prior to it? (Does it matter?!)
They bring gifts scholars see them as signifying the Messiah, Gold – King, Frankincense – God, Myrrh foretelling death.
All in one way or another precious, quite possibly funded the escape to Egypt to escape Herod they returned about 2 years later and went back home to Nazareth.