here's a very thin but very blurred line differentiating between grant writing and proposal writing. When you write a grant, it's mainly called a grant proposal. However, both types are basically intertwined with each other and it basically becomes a proposal and a grant proposal on one single document. The major and only difference between the two is a grant proposal is a proposal that requests a grant required to fund something.
Say that you want to build a museum of some sort. It's going to be a grant proposal. The proposal part is going to come first because you're explaining the nature of the museum, the reason for the museum, what's going to be inside the museum, and so forth. You're going to have to simplify that proposal.
From there, you write up the grant proposal afterwards due to getting the neccessary funding. When you write a grant proposal, you're going to have to get the cost structure down. You're going to explain what the funding is going to be used on. If you don't explain your reasons, chances are you're not going to get the grant. They're going to want to know what you're going to be using that cash for. So, keeping them in the dark is not a good idea.
A general proposal doesn't require any grant requests. But it might require funding requests. For example, if you own a martial arts dojo and you propose hiring an extra instructor or two, you're going to need the necessary funding for their payroll. If you want to teach something new, your probably won't need funding for it.
Another idea of a general proposal is if you're working for some place and request a change in policy. That too counts as a general proposal.
Overall, how your write a grant proposal is about the same how you would write a general proposal and vice-versa. Only difference is you're asking for money with a grant proposal. But writing a grant proposal is a bit more tedious than a regular proposal. As mentioned, you're going to have to go over the cost structure, budgeting, etc. A generic proposal and be directed to one group/place/person while a grant proposal can be directed towards numerous people and entities.
First step to writing either a generic or grant proposal is to do your research. Find out what you want to propose. If it requires funding, figure out what you would need the funding for. I mean go into detail on it. However, be simple and direct on it. Make it at a page long and no more than two pages. Not many people are willing to be reading things that go over five page to twenty pages at least.