Here is my attempt at translation of the accepted answer to the duplicate (your second link):
(limiting the scope to similar meanings only)
пытаться - (try) to perform directed actions in hopes to obtain result.
пробовать - to try, while being unsure in usefulness of the chosen approach
стараться - while sticking to the chosen approach, expend the efforts to obtain the best result.
The difference between your words is the same as between the nouns попытка and старание. A more suitable translation for the latter that I could find is 'assiduity' (the former is, of course, 'attempt').
Hence you can translate "пытаться" as "to try, to attempt" and "стараться" as "to apply oneself, to strive, to exert oneself"
http://en.glosbe.com/ru/en/ seems to have those.
Я пытаюсь придумать примеры. - I am trying to come up with examples.
Он старается выглядеть счастливым. - He strives to look happy.
Она всячески старалась не показать вида. - She endeavored at all cost not to show it.
Вчера мы пытались доказать это. - Yesterday we attempted to prove it.
Я стараюсь не подводить друзей. - I take pains not to fail my friends.