Although extend and expand can be used interchangeably in some contexts, extend applies to things that are being stretched out, while expand applies to things that are spread out. One implies length; the other area.
If you extend your arm, for example, you stretch it out, making it longer. If your waist expands, it’s getting larger. As a business expands, or gets larger, it may extend its opening hours.
Extend comes from a word meaning “to stretch out, lengthen.” (Latin extendere, “stretch out,” from ex– “out” + tendere, “to stretch.”)
Expand comes from a word meaning “spread out, spread flat.” (Latin ex– “out” + pandere “to spread, stretch.”