We use "scare" when we say like: "Don't scare me!" In the sense of scaring someone.
We use "frighten" when we say like: "They frighten the cat!" In the sense that they were sending away the cat.
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About big and Large, when we say that something is big, we say that is big. Large, we use in the case of sizes. Both word are adjectives, so... The dictionary can help us:
*Large: adjective
1. of more than average size, quantity, degree, etc.; exceeding that which is common to a kind or class; big; great: a large house; a large number; in large measure; to a large extent.
2. on a great scale: a large producer of kitchen equipment.
3. of great scope or range; extensive; broad.
* Big: adjective
1. large, as in size, height, width, or amount: a big house; a big quantity.
2. of major concern, importance, gravity, or the like: a big problem.
3. outstanding for a specified quality: a big liar; a big success.