Tense – Simple Past vs. Present Perfect: Key Differences

Context, context, context!

Briefly: the simple past is used to narrate past events. The present perfect is used to mention past events which give rise to a present state which is of present interest.

The children played in the sandbox for a while, then moved to the swings. At four o'clock their mother called them inside because it looked like rain.

The children have played in the sandbox and left their toys there. Tell them to go bring their toys inside.

However, the second could also be expressed with a simple past, and would probably be expressed with a past progressive. Play is an activity verb, which doesn't accommodate the perfect all that well. This example, with a telic verb (one which has a distinct change of state in its meaning) may be more instructive.

The children finished their chores, then went outside to play until their mother called them in.

The children have finished their chores; I am going to let them go outside and play now.

There's a lot of confusion around this, and a lot of half-true "rules" are taught.

The actual rule for the present perfect is fairly simple. The present perfect is a present tense, designating a present situation, so it cannot be used with a temporal expression which does not include the present, the moment at which the sentence is uttered.

Consequently:

^okThe directors have met is acceptable, because there is no temporal modifier. This merely asserts that the consequences of the fact of their meeting (whatever those consequences are) are now in play.

^okThe directors have met this week is acceptable, because the temporal modifier this week designates a timespan which includes the present: it runs from the beginning of the current week right up to the moment of speaking.

^∗ The directors have met last week is not acceptable, because the temporal expression last week designates a timespan which lies entirely in the past, ending with the beginning of the current week.

Note, however, that an entirely past temporal expression may be included in a present perfect sentence if it is 'bracketed' with commas or dashes or parentheses; it is then understood as a 'supplement', not integrated into the sentence but added to the sentence as an afterthought.

^okThe directors have met—just last week, as a matter of fact.

ADDED:
DamkerngT points out that you conclude that use of simple past with an indefinite temporal expression is incorrect. This is not the case. The simple past can be used with no temporal or with indefinite temporals:

^okThe directors met.
^okThe directors met sometime.
^okThe directors met before lunch.
^okThe directors met after that.

The only sort of temporal which cannot be used with the simple past is one which cannot be interpreted as lying entirely in the past, such as now or currently or tomorrow.