The double spend attack is covered in full in the entry Double Spending, which explains the problem, how blockchains prevent it and notable incidents. This page gives a short definition and explains the different names.
A double spend attack is a deliberate attempt to use the same digital coins for two payments, so that a merchant or exchange delivers goods or funds for a payment that later disappears. Because digital files are easy to copy, preventing this was the central challenge for digital cash, known as the double-spend problem. Blockchains solve it by keeping a shared record that every node checks. Attacks remain possible in some cases: a merchant who accepts a zero-confirmation transaction may be tricked by a conflicting transaction, and an attacker controlling most of a network's mining power or stake can rewrite recent blocks in a 51% attack, as happened to several smaller proof-of-work coins. Waiting for more transaction confirmations reduces the risk.
"Double spending" names the act or problem, while "double spend attack" stresses that someone is doing it on purpose. Both describe the same thing, so this site keeps one main entry.