I was trying to understand the difference among those two forms, but I am not sure about it. Could somebody provide me some example and explain it to me?
According to this page:
といえば and というと, in the sense of "speaking of" are essentially interchangeable (though there are other uses of といえば), but that といえば is often used when remembering something and you use というと when you want to ask for clarification about something.
The example given on that page is:
Here one should not use といえば.
This is used when someone else will say something and you are going to follow or to do.
like "「どちらかと言えば出かけたい。」→ 「If anything I would like to go out.」"
This is used when you will say something and you are going to follow or to do.
like "「どちらかと言うと行きたい。」→ 「I would rather go if I say something.」"
I agree with Michael Gignac that the link is useful, but I think that 言う is a special case that deserves separate attention from the simple verbs like 行く that are discussed at the link. Unlike simple verbs like 行く, 言う can be used not just as "say" as in "I will say something", but also in a speculative context regarding future possibilities, as in "Let's say that..."
I think both と言えば and と言うと can translate as "Considering that...", but my feeling is that と言えば is weaker than と言うと, because と言えば implies that the situation is not yet totally clear. と言うと contrastingly implies that the situation is clear.
「Aと言えば」means: "Considering that A might happen..."
「Aと言うと」means: "Considering that A will happen..."
来週がダメと言えば means "Considering that next week might not be possible..."
来週がダメと言うと means "Considering that next week is not possible..."