Which situation can I use it in?

[Gość: Iron Lady]

Hi! I've heard many times two sentences in the same situation. After something
had happened one Englishman said: Have you seen that?, but another one said:
Did you see that? I'm really confused which question is correct. I would
appreciate if you helped me to understand it. Thanks a lot.

[jonathan.oakley]

Compare these 2 sentences:

Have you seen the news this week? (this week is not finished)
Did you see the news yesterday? (time is finished)

Hope this helps..:)

[Gość: Iron Lady]

What if two different person ask the same question at the same day but they use
different tenses? I thought I knew when I should use Present Perfect and Past
Simple tense, but one night one manager came to me and asked me if I had seen a
new blue legal book. A few minutes later another manager asked me the same
question using Past Simple tense. I'm confused which tense I should use, which
one is correct.

[jonathan.oakley]

Yes, sometimes English grammar can seem to be confusing. As I am
sure you know, we use the Past Simple Tense (also known as 'the
simple past')for past actions that happened either at a specific
time (in which we introduce a time phrase such as 'last
year'...'yesterday'...and so on)or for actions that can be
understood by the context.

The important thing to note is this: after the auxillary verb
did/didn't, it returns to its base form: eg Did you take it?

The present perfect can also be used when the time is not mentioned.

Have you seen the new blue legal book?
Did you see the new blue legal book?