The definition for justification is often said to be "just as if I never sinned." That definition fits well, because the true definition of justification is to prove that someone has lived in complete accordance with the law. It doesn't mean that someone has sinned, yet they have been made free, though that is the case for us. Instead, justification means that, in God's eyes, we have never sinned. Truly His promise stands true when He says in Heb. 9:12, "For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more." And just in case it isn't clear, we are justified, or made just, at our salvation (Rom. 4:25; 5:16, 18; James 2:21-23).
Regeneration simply means to be made, generated, again. When it comes to salvation, regeneration (Titus 3:5) has to do with being born again (John 3:3), made alive (Eph. 2:1), made a new creature (II Cor. 5:17), made a new vessel (Jer. 18:4), and passed from death unto life (John 5:24).