Cash-on-hand is an accounting term that refers to any cash your business has in currency, such as bills, change, and currency notes. (Fun fact: Look at any US bills you have in your wallet. You'll see the "title" is Federal Reserve Note.) If you're in the retail industry your cash on hand includes any money in your cash registers; for others it includes petty cash. "What about any savings or checking accounts or short-term investments such as money markets or bonds I can draw money from immediately?" Those count as cash on hand, too.
Cash on hand is different from current assets because cash on hand does not include inventory or accounts receivable because those categories cannot be readily turned into cash. As a consultant I occasionally visited client's offices to nudge them to pay long-outstanding bills; the steel mill client was especially fun (I left with a check in full and an order for more work). Some businesses, especially retailers, tend to have a lot of their current assets tied up on accounts receivable and inventory, so they in reality they are not as "liquid" as they might appear in common accounting ratios such as current ratio. Some retailers use factoring services that buy the retailer's A/R at a discount and take care of the collections and/or use a consignment model (think Ebay) that allows them to intermediate transactions without holding inventory long-term. The famous Harvard business case "R&R" (Mossi & Stevenson, 1987) illustrates the value of using a factoring agent in some business models.
How to Calculate Cash on Hand at the End of a Period in Accounting (Houston Chronicle, Dec 24, 2018).
Mossi, J.-C. J., & Stevenson, H. H. 1987. R&R. Harvard Business School Case 9-386-019, Boston: Harvard Business School Publishing.