Translation guide
A billfold is a small folding case for holding paper money and cards, typically carried in a pocket. In Japanese, the most common equivalent is 財布 (さいふ), which covers wallets in general. For a specific billfold style, 札入れ (さついれ) can be used, but it is less common.
wallet / billfold
Most common and natural word for any wallet.
The most common way to refer to a wallet or billfold in Japanese is 財布 (さいふ). This word covers all types of wallets, including billfolds, coin purses, and card cases. It is the default, everyday term.
General term for wallet, purse, or billfold. Used in almost all contexts.
I forgot my wallet.
I bought a new wallet.
Specifically a bill compartment or billfold. More precise than 財布 but less commonly used in daily conversation. Often refers to a simple sleeve for bills.
I use a leather billfold.
When emphasizing the long, folding style typical of a billfold (as opposed to a coin purse or compact wallet), you can use 長財布 (ながざいふ).
A long wallet that can hold bills without folding them. This is the closest equivalent to a classic billfold in Japanese fashion.
A long wallet is bulky, but it's nice that bills don't get folded.
In Japanese, 財布 (さいふ) is the default word for any wallet, including billfolds. You don't need to specify the type unless the distinction is important. For example, when asking someone to take out their wallet, you'd say 財布を出して (さいふをだして), not 札入れを出して.