Your definition is not accurate. You have been taught wrong.
First, salvation IS a free gift. Romans 6:23 - For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
Second, we "receive" the gift of eternal life (salvation) by believing what Jesus did on the cross. John 1:12 - Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God.
Third, salvation IS "offered to all". Titus 2:11 - For the grace of God has appeared that offers salvation to all people.
Fourth, those who believe in Christ ARE saved. Acts 16:31 - They replied, “Believe in the Lord Jesus, and you will be saved—you and your household.”
Fifth, those who don't accept the gospel offer (don't believe) ARE lost and condemned.
John 3:18 - Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son.
2 Thess 2:12 - and so that all will be condemned who have not believed the truth but have delighted in wickedness.
Your second paragraph about "inviting Jesus into your heart" is NOT the gospel. It is believing in Him that results in salvation.
Regarding "no fear of hell or destruction", what are you suggesting here? That salvation can be lost?
John 10:28 - I give them eternal life, and they shall never perish; no one will snatch them out of my hand.
John 5:24 teaches WHEN a person possesses eternal life: "“Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life."
Could you explain how you think a person is saved and going to heaven?
Thanks.