In Christian theology, gift and salvation mean the same thing. At least when we are speaking of the relation between God and humanity in Christ. God gives us all good things, Christ gives himself over to death, the Spirit is given- and in each of these cases, we do not receive partial things, but we receive the gift of God, that is, salvation.
But what I've said is apparently a very Lutheran thing to say. Not all denominations or Christians would confess what I have just confessed. So, for example, at baptism God bestows God's gifts, but for some, this is not the bestowal of "salvation" until the salvation has been actualized in the life of the believer through repentance and faith.
God is graceful to us. This is also the same as saying that God gives us gifts. So gift, salvation, and grace are also all semantically related. Or for that matter, so is Holy Spirit, for the Holy Spirit is the wholly gratuitous gift of God out of the love God shares with His Son.
Now to be really Lutheran- even faith is a gift. So faith itself is what we mean when we alternatively say gift, grace, salvation, and Holy Spirit.
I'm not enough of an analytic philosopher to know whether this is similar to the linguistic situation in English where multiple terms mean the same thing- car, auto, vehicle, ride, wheels- even when they sound different or convey different nuances.
Nevertheless, if faith is a member of this list- grace, salvation, gift, Holy Spirit- then faith means something very different from a biblical perspective than it does in common speech, and justification by faith something other than what many theologians, focused as they are on the human will and our response to God's initiative, would have us believe.
I have been led to some of these reflections because I've just begun to read Risto Saarinen's book, God and the Gift , but also because I've recently been discussing with someone whether or not baptism saves. I say it does. So does Luther. Apparently others do not. Baptism is a gift of God- it is so also grace, salvation, the bestowal of salvation, the beginning of faith.
Contra much of modern philosophy that no true "gift" can be given, because, for the philosophers, there are always strings attached, it is a dogmatic assertion of theology that a gift, a true gift, can be given, because God can give Godself, and the Christian God bestows gifts by bestowing Himself- so God is gift, grace, faith, salvation, Father, Son, and Holy Spirit. Whatever our reception of the gifts of God is, it is simply our participation in a gift already given, nothing more and nothing less, so that our reception of the gift becomes in fact part of the gift itself.