I'm not so sure that meditation practice helps with mindfulness as they are not the same... with meditation you "allow" all the thoughts to "flow through" and if you find yourself focussing on one, you stop yourself and calm and continue to "allow" so you can relax and be at peace.

Mindfulness is stopping those intruding thoughts and staying focussed upon what is the task at hand.

As for the "big picture" I also disagree...but maybe it was just in the note taking that erred?

Mindfulness is blocking out the rest of the world while focussing upon "one" item. Now that "one item" might be a conversation with another person...so yes, the "big picture" might be to be mindful of your surroundings, where you are (you wouldn't want to mention some things in a busy public place, for instance), with whom you are speaking, how you can compliment them...etc. But one would not be mindful if they were trying to keep track of all the people and their outfits and conversations and why the bus just beeped it's horn out in the street or the rail that just went over...

Does this help with the difference?

And yes, it takes time to become better and better at it and I daresay few fully succeed (we're all human). But I've found it enriches my life. Besides, scientists have declared that multi-tasking is harmful to the brain.
( I really can't believe that since it performs thousands of transactions a second...but it might be harmful to our psyche and conscious minds!) I know that being mindful is less stressful than multi-tasking, for me anyway.

Be well.