Yes, two totally different styles! Not an easy gel.
Why don't you sit down and talk to her about your motives. Discuss that the way you have learnt to be and feels natural means that you like to plan and there are advantages to that approach.
But that you've also noticed she is interpreting that approach as controlling, when that is not actually true.
Tell her that you understand that as she naturally leans towards the spontaneous, maybe your plan ahead approach does feel controlling, but that just isn't where you're coming from.
Tell her you recognise a spontaneous approach also has it's advantages, you can roll with the changes and do things on the spur of the moment, but the flip side is that sometimes that approach can catch you out when unanticipated things cause delays/problems and there isn't time to recover it.
The planning approach has it's advantages, looking things up in advance can buy you time to make a plan B if plan a isn't possible, fewer emergency bail outs needed, but, those who are wired that way, can find it harder to pivot, are less flexible.
Recognise the strengths on both approaches.
Maybe you could agree between you, that both approaches have their uses.
All her to understand that you find it hard to switch at a moments notice. This doesn't mean you're trying to be difficult, you are just wired that way.
Meanwhile offer her the understanding that her way can be useful, that if she is happy to accept it comes with the risk of suddenly needing bailing out, that you respect her wish to run that risk. But also that, her choice to take that risk is fine, you will back off and do trying to rescue her from herself in advance... But likewise if the emergency bail out she needs, can't be promised as your day is more mapped out than that, and whilst your willing to help her in your heart, it isn't always practical. So this freedom to do things her way must be done with the knowledge that instant fixes can't always be given by you.
Meanwhile don't forget that ALL teenagers are quite bad at planning ahead compared to the adult version of themselves.
Also, both extremes if either approach are a bit of a pain, and ideally life would include a blend of either depending on what is going on. So if you are both a bit polarised you could both do with trying to appreciate the benefits of the others way.
If you can try to have that conversation and help her recognise this, and at least not assign a malicious motive to your style, but recognise you are just a different person, you would be on the way to better mutual understanding.
If she is very reactive to you now, after all you've both been rubbing each other up the wing way for some time now, you may need to thaw things somewhat before a constructive conversation can happen... But you can at least see it as a goal and work you way towards it
Having a plan, might make you feel less like it's speaking out of control, and more like you are at the when of your ship again and you need to bring your DD into this understanding with you.
Make sure you are clear that all your attempts to discuss this are because she is important to you and you think that you have both been making mistakes but that you believe you can both enjoy a better relationship of some misunderstandings (on both sides) can be resolved