I think, even in U.S., the usage varies by regions. In my region, Virginia, many companies use a term "Accounting" for a department that processes bookkeeping, issues financial statements, tracks departmental/project budgets and expenses.

Here, Accounting Department is a place where recording and reporting are performed. For smaller companies, accounting department often does not exist and finance department performs all-things-money.

As to Accounts Department, many companies in my region use that term for a department that is transactional such as sales, Accounts Receivable, and procurement, Accounts Payable, although many companies have AR and AP teams as part of accounting department to track and render transactions that sales/procurement departments report. Sales and procurement employees manage customer accounts and vendor accounts so they often have a job title that includes the word "accounts"--e.g. Accounts Manager.

This is not related to your question but Accounts Management is usually separated from Accounting because it is considered dangerous to have a single person/team to have an authority over all of actions, records, and payment processing for sales/procurement because such power allows a person/team to commit fraud by manipulating prices, invoices/receipts, and payment amounts.

In small companies both "Accounts Department" and "Accounting" are used here in the US. The former is often split into "Accounts Payable" and "Accounts Receivable", which I suppose due to some differences in whom they need to work with, and in what manner. It's often represented by a single person managing all the work.

It likely differs from company to company, and once established, rarely changes, I would think.

The expression "Account Department" is not in use most likely because that subdivision (even if represented by a single employee) handles multiple accounts.