Both of these words mean to get bigger, or to make something bigger.
Extend has more the sense of making something longer in one direction, whereas
expand gets bigger in all directions:
▶️ You extend a TV antenna.
▶️ A balloon expands when you blow it up.
▶️ You extend your arm.
▶️ A pregnant woman’s belly expands.
We also use extend, not expand, when making a period of time longer:
▶️ extend a visit
▶️ extend a deadline
We use expand when talking about businesses or areas getting bigger:
▶️ The company expanded its operations to five additional countries.
▶️ The town is expanding – many new houses are being built.
▶️ The bookstore plans to expand its range of products to include CDs and
DVDs.