MDI vs SDI

MDI (Multiple Document Interface) and SDI (Single Document Interface) are different interface designs meant to handle documents within a single application. MDI allows an application to contain child windows per document, while SDI enforces one document per window.
Neither approach has much effect on performance or stability: despite the intuition of two SDI applications as being separate entities, they are very often still implemented as a single process. Similarly, an MDI interface can be implemented as multiple processes (Google Chrome being a prime example).
It's also worth noting that tabbed interfaces, although matching the description of MDI, often don't show multiple documents at the same time in the same window, and universally support multiple top-level windows as well.

Differences

MDISDI
Maximize all documentsMaximize parent windowCan only be implemented through special code or through a window manager that can group windows
Switch between documentsUsing special interface inside parent windowThrough task /window manager
Multiple DesktopsYou can only stretch the parent window and try to organize individual windows manuallyEasily done
Multiple MonitorsYou can only span the parent window and try to organize individual windows manuallyEasily done
GroupingNaturally implementedPossible only through special window managers
Switch focus to specific documentEasily handledDifficult to implement