The meanings of the tenses are the
same in BrE and AmE.
It's just that occasionally Americans feel that time periods are finished sooner than their British counterparts, so Americans
sometimes
choose the past (feeling that the time period in question is finished)
where the British might choose the present perfect (feeling that the
time period in question is still in effect) -- even when they are both
describing the same situation. This does not happen in all cases,
however. In fact, in the majority of cases, both speakers would
probably choose the same tenses.
This isn't really different from the case when any two people (whether
American or British) view an event differently. The words still
mean the same thing, but different words are used depending on how the
person views the situation.
In your place I would not let these considerations occupy a great deal
of time and thought. It's a waste of time to attribute any great
importance to these tiny differences.
A much more important factor is that you don't mention a specific time
if you use present perfect. And that is true of both AmE and
BrE. For example,
I have gone there yesterday is wrong!
CJ