I admire anyone who can persevere on a long-term basis in terms of staying true to the goals they have set. I'm proud of the athletes who I coach because of the way they push themselves as evidenced by their motivation on a day-to-day basis, such as heading out the door for early morning workouts in the dark (and often cold conditions), or staying committed to the workouts after a long, stressful day at the office. And so I appreciate when runners show up to the track ready to put in hard work even when they don't have their A-game that day. I'm proud of them for prioritizing their health and a physically active lifestyle. These are good practical definitions of "pushing yourself."
What does "pushing yourself" mean? It means being motivated, which means being committed to put in the hard work when it's time do to so. If you want to call this mental toughness then so be it. Mental toughness has as much to do with your dedication to training on a day-to-day basis as it does with running fast at the end of a race. I never want an athlete I coach to be consumed by their running/training lifestyle, but there is a mentally healthy, performance-related benefit to being committed to holistic approach of training (massage, PT, ST, XT, stretching, sleeping well, etc) on a year-round basis.
It's my job to make sure runners don't push themselves outside of their boundaries too soon or too often, so "train smarter, not harder" is another good mantra. As you enter your peak race season, make sure you are honest with yourself about how hard you are pushing yourself!