It ends at a specific chapter, but I can't recall exactly off the top of my head. You might want to check online manga forums or dedicated One Punch Man fan sites for the precise chapter.
One Punch Superman was finished. Although the plot of the first season was very exciting, the animation production company did not seem to have any plans to continue the second season. However, fans of One-Punch Superman could still continue to enjoy the story through comics, novels, and other media.
In general, the One Punch Man manga does pick up from season 2. However, the anime sometimes makes adaptations and changes that might not be exactly the same as in the manga. So, while the main storyline continues, there could be nuances.