These two terms were completely unknown to me until a couple of years ago. I finally found an explanation from the WELS.net site that helps me to understand:
Question: In the Lutheran Churches we are correctly taught salvation thru faith alone. Other Protestant Churches all claim the same teaching of salvation thru faith. However, some denominations, especially Baptists teach that you are saved by asking Jesus into your heart to forgive you. Seems to me they are saying that praying and asking for forgiveness saves you. Where is saving faith in their decision theology. I'm confused.
Sounds like to me they do not include faith in conversion.
Answer: Perhaps the best starting place to answer your question is to remind ourselves that, among professing Christians, there are two different approaches to the doctrine of conversion and salvation: monergism and synergism. And there are variations within those two groups, monergists and synergists.
Monergists (really only strict Calvinists and Lutherans among major church groupings) teach that God alone is the one who saves and that humans have no active role in coming to faith (conversion). Unfortunately, Calvinists also teach that God alone and unilaterally decrees and determines who will be lost, and that makes them different from orthodox Lutherans. But they and we share the conviction that God creates faith and causes the unbeliever to become a believer without any merit, worthiness, or cooperation on our part. That's monergism.
Synergism, on the other hand, teaches that humans have some role to play in conversion and being saved, and that people in some way "work together" with God to bring this about in individual lives. But aside from this basic premise, synergists differ in how they believe the human being contributes to conversion and to what degree the person cooperates with God in being saved. Roman Catholics are synergists (some prefer the term semi-Pelagianists) and so are many Evangelicals (including professing Calvinists, which makes it really confusing). And some who bear the name Lutheran are also synergists (but are Lutherans in name only).
Some synergists teach that some sinners cooperate with God by resisting God and his grace less than other do, and other synergists say that some sinners respond more favorably to God's grace than others do and therefore are saved. And in the example that you gave, namely that of decision theology, synergists treat faith as something the sinner comes up with in response to and in cooperation with God's grace. Faith is ultimately being treated as a cause or condition of salvation, a part of the cooperative effort that the human being is to some degree responsible for. It's sort of like saying, "God does his part by providing Jesus as the Savior and informing us of that Savior, and we must do our part by believing in the Savior and deciding that we will trust him--then we will be saved."