In one sense, they are the same. Heaven is a place where time will not exist as we know it on Earth. This means life in heaven will be eternal; no more death. Heaven is a destination Jesus promised for all who put their trust and faith in him as their Savior. He is the only way to that eternal place of peace, joy, abundant love and eternal life. In John 14:3, Jesus said, “I go to prepare a place for you, so that where I am you may be also.” That is one of the greatest promises ever made to mankind. It’s called God’s grace. God giving us something we did not deserve and never could earn by our own good works.
In another sense, eternal life is much more than heaven. Jesus said, “Now this is eternal life; that they may know You, the only true God, and Jesus Christ whom you have sent.” ( John 17:3) What this simply means is that when you have an intimate personal life with Jesus as your Lord and Savior you have eternal life here and now. Then you will experience an abundant and exciting adventure with the one through whom God created the entire universe.
As you let Jesus transform your life into his image you will see and experience life as you never could have imagined. Then you have eternal life and your spirit/soul will never die. It will go to heaven where one day you will get a glorious new eternal body. That is the good news of the gospel of Jesus Christ.