I gather from your question you are not asking how one is saved or what one is saved from, but your question seems more to do with linguistics and hermeneutics. That is to say, how can they translate the common word for save or salvation to mean all those other words like deliverance, preserve, heal, & etc? We often come to the word “save” or “salvation” and immediately jump to the theological definition of the word as it applies to eternal life, but the word does have a root meaning and an extra-biblical root. The word in the Hebrew is yashameaning to save, deliver, help, victory & etc. Sometimes the word for “life” hayah is translated saved. How do translators determine what to translate the word as? Words have a basic meaning, but it is context that determines exactly what it applies to and hence the meaning. For example, the word for salvation is the Greek soteria and can mean preservation from danger, disease, or death. Hence it is sometime used to mean physical salvation or deliverance.
Within the realm of the Bible, words are analyzed in their context to build what is known as a Biblical Theology or a Systematic Theology. Biblical Theology is restricted to what specifically comes from the Bible, while Systematic Theology is built by both the Bible and external sources and disciplines. The word for saved in the Greek New Testament is the verb sozo and can mean preserve or rescue from natural dangers and afflictions. Context determines how to translate the word and what it means in detail. There are some who say words don’t mean anything except in context, but that is not correct. The basic word is still restricted to a certain range of meanings, and it is made precise when placed in context.
Understanding this is important and in some Churches a lack of understanding has led to great error. For example, in some Churches, one cannot be saved unless they confess in front of the whole congregation, or unless one is publically baptized in water, or speak in tongues. This kind of error comes from a lack of basic hermeneutical principles, chief of which is context. It is just like your grade school teacher taught you, when reading ask the five “W’s:” who, which, what, why, and when. Answering these questions will make the writing clear and clear up some of these errors. One big mistake when reading the Bible is the called Cross-reference interpretation, where the reader searches for uses of the same word or similar passages, words, or phrases anywhere in Scripture assuming the word means the same thing everywhere without regard for the immediate context. So, for example, even though the Bible clearly states many times (over 100 times) salvation is received by belief alone, at times there are passages where salvation is used in the same sentence with baptism, but context gives us clues as to why. The historical, cultural setting cannot be thrown out when reading the Bible, and when the word saved is used throughout the Scriptures, some 1500 years of history and various cultures and authors have to be brought into consideration.
From the basic Greek word sozo and a concordance one finds the word means to save from death (Matt. 14:30), bring out safely (John 12:27), to free from disease or demonic possession (Matt. 9:22), but the word has a special spiritual significance as it relates to rescue or preserve from eternal death, from judgment, sin, to bring salvation, or bring to salvation. Categorizing the word theologically, that is to say, organizing the teachings of the word as it specifically relates to eternal life for mankind, one finds that salvation is something that God does. Salvation is of the Lord (Jonah 2:9; Ps. 3:8), it means being saved from the guilt and penalty of sin (Rom. 6:23), and occurs when one believes the gospel of Christ (Acts 16:31). The gospel being the message that Jesus (Jesus is the Hebrew word for savor) Christ, God came in the flesh, died on the cross, was buried and resurrected (1 Cor. 15:1-5).
Salvation has three tenses: the past – we have been saved (Eph 2:5,8), relates to the release from guilt and penalty of sin and is accomplished the moment one believes the gospel. The present – we are being saved (Phil. 1:19; 2:12-13) relates to the release from the power of sin (John 17:17; Rom. 6:14; 8:2; Gal. 5:16). The future – we will be saved (Rom. 13:11) is the completion of release from the presence of sin.
This part of the theology not only includes context, but grammar. The verb tenses speak volumes – “we have been saved” is a Greek perfect passive, meaning the action was performed by an external agent and it occurred in the past and is complete. This of course speaks of the character of our God. Our God is in active control, bringing eternal life to all who believe, and He will keep them safe, preserved forever (Rom. 8:28-29) – for they possess eternal life. May God bless you in your studies.