He has started taking antidepressants.
It'll be used in the case when he has recently started the process of taking those antidepressants.
He has been taking antidepressants.
It'll be used to signify that a significant time has passed since he started taking the antidepressants.
He has taken antidepressants.
This and the first one are similar in context of time-frame. But this will just mean that he has taken the antidepressants for a particular time while the first one will mean that he either has a habit of taking antidepressants or he has been prescribed for it.
He took antidepressants.
Similar to the previous one. The tense here is past, where as in the has taken case, it was past-participle.
For all practical purposes, there's really not much difference in meaning. Either one could be used to announce the appointment of a new manager.
Let's assume we appoint Renee as the manager today. Our Regional Director comes into the office to make the announcement:
Renee is appointed as Manager.
Tomorrow, an absent co-worker comes into work, and asks:
Who was appointed Manager?
(This co-worker uses the past tense, because the appointment happened yesterday). I might reply:
Renee has been appointed has manager.
So, why didn't I say, "Renee was appointed as the manager" instead? Because Renee is still the manager! I could use was – it wouldn't be incorrect – but it might lead to some confusion. I can imagine my co-worker saying:
Was? What do you mean, "was"? Isn't Renee still the manager?
The further the event moves into the past, though, the more natural was will sound, because we're talking about an historical event, rather than a current event. Imagine we fast-forward two years into the future, and I am training a brand-new employee:
Tracy was our manager until two years ago, but then he retired.
Oh, then what happened?
Then Renee was appointed as Manager.
Renee's appointment is no longer a current event, so "has been" doesn't sound right in that context.
This looks a lot like the present perfect continuous tense, except that tense uses a verb that ends with -ing:
Our company president has been appointing a lot of hot shots with very little experience.
I'm don't think your sentence is quite the same thing, though, because of how we'd parse your original sentence. It's not:
Renee (has been) (appointed) (as Manager).
but:
Renee (has) (been appointed) (as Manager).
So, we're really dealing with passive voice here, not the present perfect continuous tense. In active voice, we would say:
The company president has appointed Renee as Manager.
or, the Regional Director might say:
We have appointed Renee as Manager.
Best Answer
Another way to phrase these sentences would be:
I'm not an expert in explaining this in fancy terms, but I hope you get the difference from these examples.