Computed values and methods are very different in Vue and are definitely not interchangeable in most cases.

Computed Property

A more appropriate name for a computed value is a computed property. In fact, when the Vue is instantiated, computed properties are converted into a property of the Vue with a getter and sometimes a setter. Basically you can think of a computed value as a derived value that will be automatically updated whenever one of the underlying values used to calculate it is updated. You don't call a computed and it doesn't accept any parameters. You reference a computed property just like you would a data property. Here's the classic example from the documentation:

computed: {
  // a computed getter
  reversedMessage: function () {
    // `this` points to the vm instance
    return this.message.split('').reverse().join('')
  }
}

Which is referenced in the DOM like this:

<p>Computed reversed message: "{{ reversedMessage }}"</p>

Computed values are very valuable for manipulating data that exists on your Vue. Whenever you want to filter or transform your data, typically you will use a computed value for that purpose.

data:{
    names: ["Bob", "Billy", "Mary", "Jane"]
},
computed:{
    startsWithB(){
        return this.names.filter(n => n.startsWith("B"))
    }
}

<p v-for="name in startsWithB">{{name}}</p>

Computed values are also cached to avoid repetitively calculating a value that doesn't need to be re-calculated when it hasn't changed (as it might not be in a loop for example).

Method

A method is just a function bound to the Vue instance. It will only be evaluated when you explicitly call it. Like all javascript functions, it accepts parameters and will be re-evaluated every time it's called. Methods are useful in the same situations any function is useful.

data:{
    names: ["Bob", "Billy", "Mary", "Jane"]
},
computed:{
    startsWithB(){
        return this.startsWithChar("B")
    },
    startsWithM(){
        return this.startsWithChar("M")
    }
},
methods:{
    startsWithChar(whichChar){
        return this.names.filter(n => n.startsWith(whichChar))
    }
}

Vue's documentation is really good and easily accessible. I recommend it.

Here’s a breakdown of this question.

When to use methods

• To react to some event happening in the DOM
• To call a function when something happens in your component.
• You can call a method from computed properties or watchers.

When to use computed properties

• You need to compose new data from existing data sources
• You have a variable you use in your template that’s built from one or more data properties
• You want to reduce a complicated, nested property name to a more readable and easy to use one (but update it when the original property changes)
• You need to reference a value from the template. In this case, creating a computed property is the best thing, because it’s cached.
• You need to listen to changes of more than one data property