"To wait'' is more passive. When you wait, you are doing exactly that, just waiting for something to happen. ex: wait for the bus - you can think of someone sitting on a bench just waiting for the bus to arrive. ''anticipate'' is more like 'look forward to/ predict/to expect', so instead of just waiting for something to happen, you imagine or predict the possible scenarios and results. "She anticipated rain, so she brought an umbrella" "She anticipated a delay for her bus, so she brought a book to read, while she waited" :)

"Anticipate" and "foresee" are near-synonyms. "Anticipate" suggests hope, and is often found in the two-word combination "eagerly anticipate." "Foresee" suggests prediction. In English, "wait" does not carry ANY feeling of hope or pleasant expectation. It suggests boredom, passivity, emptiness. Dr. Seuss wrong a wonderful "children's" book, "Oh, The Places You'll Go!" which is a celebration of optimistic anticipations of future life and career. In this book, a few pages are devoted to "The Waiting Place," a miserable place--a metaphor for periods of time in your life where you get stuck: headed, I fear, toward a most useless place. The Waiting Place... ...for people just waiting. Waiting for a train to go or a bus to come, or a plane to go or the mail to come, or the rain to go or the phone to ring, or the snow to snow or waiting around for a Yes or a No or waiting for their hair to grow. Everyone is just waiting. Waiting for the fish to bite or waiting for wind to fly a kite or waiting around for Friday night or waiting, perhaps, for their Uncle Jake or a pot to boil, or a Better Break or a string of pearls, or a pair of pants or a wig with curls, or Another Chance. Everyone is just waiting. NO! That's not for you! Somehow you'll escape all that waiting and staying. You'll find the bright places where Boom Bands are playing.

Anticipating is usually more positive. You anticipate something that is pleasant, or useful. You 'look forward' to it. 'I am anticipating a visit from my children'. It can also mean to prepare for something, or to get ready for something, e.g. 'Defensive driving is about anticipating potential accidents before they happen'. Waiting however is just doing nothing, or doing something else, before the thing you are waiting for. You go to the doctor, and wait until she is ready to see you. You write a question on italki, and wait for answers. Waiting can involve anticipation, but not necessarily.