Many laptops use a dedicated charging control chip plus 2 or 3 MOSFETs to control the flow of power between charger/AC supply (typically around 18 - 24v), battery, and the main motherboard switch-mode power regulators (eg backlight, 5v, 3.3, and now often 1.8v and down to sub-1v) . Usually there is a permanently-on low-current supply (typically 5 or 3.3v) for the charging control, soft-start, wake-on LAN/RTC, sleep/hibernate and other 'powered-off' actions.
The block diagram below shows the functions in a TI BQ24721 charger/battery management controller - but many IC manufacturers produce similar devices. The ATX/ACPI functionality in a desktop is quite crude by comparison.