You didn't know it @AmberFL, but this statement has been stuck in my head almost all day.
Let me explain. Earlier I spent ~1.5 hours running in a cold hard rain and frankly it kinda sucked. My mind started wandering (as it often does when I run), and I was asking myself why I was out there running in such lousy conditions. That's when determination popped into my head and that's when I remembered this thread.
It made me think of all the folks that say "I just don't feel motivated to do XYZ today". I was thinking on my run though that I wasn't feeling motivated either, but I was still out there running (and partly questioning my sanity). It occurred to me that it was in fact determination, stubbornness, perseverance, resilience or just plain refusal to quit. I wasn't out there because I wanted to be, or because it was fun, I was out there because I HAD to be to be.
I guess my point here is that I think of motivation as fleeting. It's the spark that sets me off to accomplish hard things and set lofty goals, but it's determination that keeps me going toward reaching those goals day-to-day.
I short, your statement above was perhaps more spot on and profound than you might have realized. Of course it's your determination to do hard things that's keeping you going. That's perfectly normal and as it should be!
Anyway, thanks for motivating me through a hard workout!