Was The Order of Merlin a force like The Order of the Phoenix which was created by Dumbledore to fight with Voldemort?
If no, then what is the difference between both those 'Order's?
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The Order of Merlin was an organisation founded by Merlin in the Middle Ages, which was meant to further the belief that wizards and witches should not use magic against Muggles, but help them instead.
So yes, it was an organisation not unlike the Order of the Phoenix, although their goals differed, and the Order of Merlin might not have been a secret society like the Order of the Phoenix.
This information comes from the Chamber of Secrets video game by Electronic Arts, and/or actual physical cards that accompanied Chocolate Frog candy purchasable in real stores. Those two sources both feature Famous Witches and Wizards Trading Cards (also known as "Chocolate Frog Cards", which also make appearances in the novels and movies). Together, these amount to 101 trading cards that were written by J.K. Rowling herself according to The Harry Potter Lexicon (and the Harry Potter Wiki as a consequence considers this information as "tier-one canon"). The text of these cards can also be read at the Lexicon.
The Order of Merlin of recent times is an award that commemorates Merlin and which is bestowed upon wizards and witches that do great things for the wizarding world. It was created by the Wizengamot in the 15th century, and it's not known whether it's related to the actual organisation Merlin headed or just named after him.
The Order of Merlin is an award which basically functions as the wizarding equivalent of the Muggle honours system. From Pottermore:
The Order of Merlin, commemorating the most famous wizard of his time, has been given since the fifteenth century. Legend says that the green ribbon, on which the First Class Order hangs, is to reflect Merlin’s Hogwarts house...As often happens with such highly coveted awards, Ministry of Magic favourites seem to receive the Order of Merlin, especially the higher classes, more often than one might expect.
(Pottermore, "Order of Merlin")
So it's a prize or award, given to superlative witches and wizards like...Gilderoy Lockhart.
"Gilderoy Lockhart, Order of Merlin, Third Class, Honorary Member of the Dark Force Defence League and five times winner of Witch Weekly's Most-Charming-Smile Award..."
(Chamber of Secrets, Chapter 6, Gilderoy Lockhart)
Here JKR seems to be using the meaning of 'order' as in a medal or symbol of honour. From Wikipedia (credit to tobiasvl for finding this):
An order is a visible honour awarded by a sovereign state, monarch, dynastic royal house or organisation to a recipient, typically in recognition of individual merit.
As the Pottermore page on the Order of Merit makes clear, Orders were awarded in the form of a golden medal on a green, purple or white ribbon. This seems to fit the meaning above.
The Order of the Phoenix, on the other hand is an organisation.
"It's a secret society," said Hermione quickly. "Dumbledore's in charge, he founded it. It's the people who fought against You-Know-Who last time."
(Order of the Phoenix, Chapter 4, Number Twelve, Grimmauld Place)
This uses a different meaning of the word 'order', along the lines of the examples below (although quite different from them, of course). From Google:
This means order as in club or society. Another example of an order within the books is Dumbledore's Army. 'Order' here confers an implication of an underground organisation (at least for me), since the Order of the Phoenix is distinct from the Ministry and the Death Eaters. Members of the Order of the Phoenix often work secretly and discretely to achieve their aims. They are a band of brothers who are fighting for a worthy cause. 'Order' communicates all of these connotations by implication and is therefore a cooler/more creative choice of title than 'group' or 'organisation'.
Judging from the context in which the order is mentioned, the OoM is an award giving group, sort of like the group that gives out the Nobel prizes.
Like, we see mentions of 'winning an order of Merlin, first class'. This could be a rank or an award, we don't know.
The OotP, however, is an anti-Voldemort resistance group. Not the same at all.