Anticipate and expect are close in meaning, but they are not the same. Anticipate often means to prepare for something before it happens, or to act in advance. Expect means to believe that something will probably happen.
A simple way to remember it is this: anticipate involves action or readiness, while expect involves prediction or belief.
- I anticipated traffic, so I left early.
- We expect the package tomorrow.
- She anticipated questions and brought extra notes.
- They expect a strong turnout at the event.
In everyday use, people sometimes use anticipate to mean expect, especially in formal contexts. Still, the clearest contrast is useful: if you mean someone prepared ahead, choose anticipate. If you mean someone thinks an outcome is likely, choose expect.
That difference makes your writing more precise and easier to understand.