When powering household devices, does a power adapter have a preset (or in some cases user-defined) voltage, while the device (while turned on) "selects"/draws whatever amount of amperage it needs at any given time?

Part of why I ask is while searching for replacement power adapters for speakers, one device says it needs 6V DC input and also says max power input is 4W. The adapters I find online have labels with a max amperage listed but a set voltage or selectable voltage. This makes me think amperage can vary based on device use, but voltage is set by the adapter; the voltage needs to be correct but the ultimate power draw can be limited (to under 4W, or with 6V that'd be ~500mA) as needed by the device. Is it the case that an adapter sets voltage but amperage can vary based on device needs/"request" of electricity?