Question: Are there some differences in sentences 

> 
> *You've got to be strong*.
> 
> 
> 

and 

> 
> *You should be strong.*
> 
> 
> 

Are they the same?

Answer: 
There are things we *need* to do, and there are things we *should* do. Think of "needs" as requirements, while "shoulds" are recommendations. 

So, if you want to convey that it is absolutely essential to remain strong, use one of these:

> 
> We need to be strong.  
> 
>  We must be strong.  
> 
>  We've got to be strong. 
> 
> 
> 

On the other hand, if you are recommending that we remain strong, use one of these:

> 
> We should be strong.  
> 
>  We ought to be strong. 
> 
> 
> 

And if you want to express confidence that our strength will not falter:

> 
> We will remain strong.  
> 
>  We shall remain strong.
> 
> 
>
Their meanings are the same, but their use contexts are slightly different. 
While both mean roughly the same thing ('you need to become stronger'), 'you've got to' is more impassioned and more personal (and slightly more informal) than 'you should'.