What's the difference between tror and synes?

What's the difference between tror and synes? This is a question I repeatedly hear from students at varying stages in their Danish Danish language journey. The words tror and synes both translate as think in English and are arguably two of the most confused words due to any number of small nuances in the language. 

Here you can read, in depth, the distinctions between the words tror and synes so you can feel confident that you're using them correctly. 

Tror 

Verb Conjugation: Tro, at tro, tror, troede, har/havde troet

 

 
A belief
The simple answer is that tror is your belief. There are, however, many nuances when using tror. Let's go through the main uses and look at some examples.
 
Religious Belief
Jeg tror på Gud. 
I believe in God.
 
Det er et spørgsmål om tro. 
It's a question of belief/faith.
Supernatural Belief, Imagination, Illusion
Tror din søn stadig på Julemanden?
Does your son still believe in Santa Claus? 
 
Troen på djævlebesættelse er stadig levende i nogle lande. 
The belief in (demon) possession is still alive in some countries.
Belief/faith in a person and/or their abilities; that a something is true
Man skal tro på sig selv. 
You must believe in yourself. ​
Jeg tror ikke på, hvad regeringen siger. 
I don't believe what the government are saying. 
Jeg kan ikke tro mine egne øjne. 
I can't believe my own eyes. 
To consider something to be true or not (about which certain knowledge exists)
Han tror ikke, at filmen udkommer i år. 
He doesn't think the film will be released this year. ​
Vi tror faktisk, at han er rejst til et andet land. 
We actually think he's travelled to another country. 
To feel/be convinced of something
Hun troede, at klokken kun var syv. 
She thought it was only seven o'clock. 
Vi tror at vi er i toget til København.  
We think we're on the train to Copenhagen. 
To have a subjective opinion about how you think someting should be. 
This final example is arguably where the line gets a little blurry between tror and synes. You'll see why as we continue.  
Pandaen tror nok at jeg er dum.
The panda probably thinks I'm stupid. 
 
Helt ærlig. Jeg tror at du skulle finde noget større. 
Honestly. I think you should find something bigger. 
You can see in the final example how it's boardering on being an opinion, but the nuance is that it's a statement based on a certain possible outcome: I think you should find something bigger (because you'll probably regret it or need more space)
 
 

Synes

Verb Conjugation: at synes, -,  syntes, har/havde syntes

An opinion
In terms of thinking, the meaning of synes is far more straight forward with fewer usages than tror.
To have a specific opinion, attitude, or interpretation of something or someone. 
Hvad synes du om poesi?
What do you think about poetry? 
 
Jeg synes, at det er meget interessant. 
I think it's very interesting. 

Synes does have some other usages, but in order to keep with the translation of thinking, I will not add them here. With that said, the main difference between tror and synes is that one is your belief (blind faith, faith in people, situations and truths, assumptions, and convictions, whereas synes is simply your or someone else's opinion