Some people will use these terms or account titles interchangeably: Bad Debt Expense, Doubtful Account Expense, Uncollectible Account Expense. The same for these terms or account titles: Allowance for Bad Debts, Allowance for Doubtful Accounts, Allowance for Uncollectible Accounts.
The "Allowance for ..." is a balance sheet account. However, it is a contra account to the asset Accounts Receivable. (Generally, the Allowance account will have a credit balance—whereas Accounts Receivable and other asset accounts normally have debit balances.) The Allowance account communicates to the reader of the balance sheet the amount of Accounts Receivable that will likely not be collected.
The three Expense account titles listed above are income statement accounts and will have the usual debit balance. These expense accounts report how much bad debt expense was incurred during the period shown in the heading of the income statement.
To gain more insight on this topic go to AccountingCoach.com's explanation of Adjusting Entries, Part 1.