Generally a marketing plan goes into more detail and depth about sales and marketing planning, offers additional strategy detail and market analysis, and does the market analysis, expense budget, sales forecast, and milestones tables. A business plan, on the other hand, covers the whole business. Business plans include marketing and market analysis, and they also cover cash flow, financing, etc.
One immediate distinguishing point: a business plan gives you real cash flow analysis and insight, plus balance sheet and ratios. A marketing plan doesn’t. If you need to deal with the whole business, you might want both, but when in doubt, try the business plan first. Lots of people in marketing aren’t responsible for cash flow, just sales and expenses. They don’t want to deal with the full financials. If you are responsible for the whole business, you want the business plan first. If you don’t manage cash flow or financials at all, you want marketing plan first.
A marketing plan and a business plan have some of the same topics and some of the same spreadsheet structures, and information should transfer easily from one to the other. For example, your sales forecast, sales and marketing expenses, market analysis, and mission statement can transfer from one to the other. After all, you do want to synchronize that information.