If a Christian struggles with the same sins they made before becoming a Christian, does that mean they aren’t really saved because they haven’t actually repented?

No; repeating sins doesn’t me we haven’t repented. We all repeat sins, and we all have certain areas in which we struggle with sin, or maybe better said, struggle with surrendering areas of our lives to God. If the area I struggle with is anger, the odds are good that I will stumble in that area from time to time. Paul very memorably said it this way: I do not understand what I do. For what I want to do I do not do, but what I hate I do—Paul, Romans 7:15. And what Paul goes on to say is that the believer are confounded by two natures: the one being that of the Holy Spirit, and the other being, as he puts it, sin living in me—Paul, Romans 7:17b. As he goes on to say, I know that nothing good lives in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. For what I do is not the good I want to do; no, the evil I do not want to do—this I keep on doing. Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it. So I find this law at work: When I want to do good, evil is right there with me—Paul, Romans 7:18-21. The idea of sanctification, of growing into the image of Christ, is that, as I mature in the faith, as I continue to fall more and more in love with the Father through the Son, the presence of His Holy Spirit in my life is going to make me more and more sensitive to what displeases the Father, and I am going to seek through Him to rid my life of those areas. That being said, until we are re-created perfectly in eternity, we will always have that internal struggle between the Holy Spirit and the sinful nature we were born with. That’s why it is so important to remember how complete the forgiveness offered by Christ is for us; Paul said it this way to the Colossian church: When you were dead in your sins and in the uncircumcision of your sinful nature, God made you alive with Christ. He forgave us all our sins, having canceled the written code, with its regulations, that was against us and that stood opposed to us; he took it away, nailing it to the cross—Paul, Colossians 2:13-14. For Christians, all our sins are gone in God’s eyes—yesterday, today, tomorrow, forever! Our sinful nature, as frustrating as it can be, is dead because of our life in Christ. In heaven, we will finally and fully understand what that means.