What is the difference between love and true love? Is there a difference?

I am having issues with my girltriend at the moment. She has been distancing from me for about a month at this point. I found out recently that she had eyes for another man, with the intent to break up with me to be with him. The night before I found out, we had an amazing conversation and both truly felt connected. After I confronted her she told me she did feel that way about him and after our previous conversation something in her mind changed and she wanted me again. To continue on in this relationship I gave her an ultimatum, Him or me. She chose me. Do you think this shows her love for me is more than him? Is it true love? When I go through tough times with someone I love, I never stop loving them even if I feel resentment, frustration, or any other negative feelings towards them. She has expressed that she has not felt love towards me for that month we have been distant. She says she chose me because she realizes what she did was wrong and what she wants is clear to her. She said she loves me, just not fully yet. I have a hard time understanding that. I would never ever do that to her in any situation. Now I'm grappling with the idea of love. Is there different kinds of love? Is loving someone only partly, still love? I see love as an unconditional emotion. No matter what happens in any situation love is always present in my eyes. What are your thoughts? Do you think this relationship is worth working on?