Question:

Why is the Redemption often referred to as "the true and complete Redemption"?

Answer: 

The expression contrasts the future Redemption with those we have previously experienced.

The expression "the true and complete Redemption" is meant to differentiate between the approaching Redemption and previous redemptions experienced by the Jewish People.  When our ancestors were redeemed from Egypt, or from the Babylonian or Persian exiles, those were temporary redemptions, followed by repeated exiles.  They concluded with the destruction of the first and second Holy Temples, which indicated that they never were the "true" or "complete" redemption.  The future Redemption, by contrast, will never be followed by another exile.

Another difference is that after the future Redemption, not a single Jew will remain in exile.  When our ancestors left Egypt, or when the Diaspora returned to build the Second Temple, not all Jews merited being redeemed.  Many remained behind in the foreign lands.  According to an opinion in the Midrash, only twenty percent of the Jewish People actually left Egypt!

However, regarding the future Redemption we are assured:  "And you will be gathered up one by one."  Even the greatest sinners, who strongly opposed the Redemption, will in the end merit to do teshuvah and return to the Jewish People, to pray to G-d in Jerusalem.  As a verse in Prophet Samuel states:  "No Jew will be left behind."

In the Passover Haggadah, we tell the wicked son:  "If he had been there (in Egypt) he would not have been redeemed."  This time, however, regardless of the circumstances, every Jew will merit redemption.  (Of course, it is recommended that each of us prepare for the upcoming Geulah to the best of our abilities.)  For these reasons, the approaching redemption will be the true and complete one.