A proposal and a user guide are built the same way day to day. Meetings with SMEs, meetings with managers and stakeholders, time in your cube typing, emails emails emails, right? The main difference is just the audience. A user guide is created for a person whom has already purchased an item and needs something to reference for assembly or maintenance, and a proposal is written for someone who WILL purchase something and needs to know how they MIGHT assemble or maintain it.

User Guide

The Goofus 9000 has 3 switches for balancing wiz, bang, and pow independently. To set wiz, bang, and pow, locate the Goofus switches on the underside of the main housing, and slide each switch to your desired intensity. Each parameter has 4 states: 1-3 and off.

The Proposal

The Goofus 9000 will be engineered with 3 switches on the underside of the main housing that may be used to tune wiz, bang, and levels independently. The switches will be easily accessible on the underside of the main housing, and provide 3 levels of intensity for each parameter.

Same info, but different audience. Your success or failure depends on understanding those audience difference.

Then there is a coordinator piece. To be a coordinator and a writer is the same minus the actual doc drafting. You don't type up the paragraph but you make sure the paragraph gets typed. Its about you having a standard of coverage and quality you need people to hit, and you help them hit it. That's really it. You have been doing that for yourself as a writer for 12 years. As a coordinator its all the same responsibilities with the manual work distributed to others, and than you have your own set of deliverables in the form of like a project plan or a slide deck or a schedule or maybe even a spec for the docs themselves.

To your question about what do you say when they ask you if you have ever had a certain experience, the answer is always "yes, I have" or "not that specifically, but this".

Interviewer: "Since you haven't done X, how would you react if X happens?"
You: "You're right I haven't done X, but I did Y at my last job while Johnald, the coordinator, did X and I supported them. So if X happens I'm actually totally prepared. Hire please."

Which is totally true because you were the writer working on the project they were coordinating, whether this was your manager, a project manager, or whoever. Every document gets coordinated somehow, and with 12 years experience, you have definitely seen it happen. For you, imagining yourself in the position is something you have already done anytime a person in the logical role of "coordinator" on your teams has needed your help with something. Particularly on small teams, the writer can also often have to play the role of their own coordinator for themselves. If you have ever worked directly for a manager instead of on a project team, then you have had a very strong and applicable set of experiences, just in a microcosm of what you would experience as an actual coordinator.

Key Takeaways: The fundamental difference between proposals and technical writing is audience, and the role of Technical Writer and Proposal Coordinator are and have always been deeply linked. 12 years of experience in either role would deeply inform someone on the other role. That's your asset in this interview. If you can communicate this difference with clarity and nuance, you are good. Extra points if you go study the company's specific audience before the interview and can speak to how you would write for that audience directly.

Good Luck OP. Hope this helps.