What is the difference between 'transferred epithet' and 'metaphor'?

In the poem 'My Mother at Sixty-six' by Kamala Das (which I have attached below), what is the poetic device in the line 'the merry children spilling out of their homes'?

I feel like it should be transferred epithet as the children are not literally spilling. The adjective which usually describes a liquid spilling out of a cup is being used to describe the children. The children are coming out of their homes in huge numbers which just looks like liquid spilling from a cup.

But my teacher said that it was a metaphor with no explanation. But I'm skeptical about that.

From what I know, metaphor is a poetry device in which something/someone is compared to something else without the use of words like/as. For eg: You're the sunshine of my life.

My Mother at Sixty-Six

Driving from my parent’s

home to Cochin last Friday

morning, I saw my mother,

beside me,

doze, open mouthed, her face

ashen like that

of a corpse and realized with pain

that she was as old as she

looked but soon

put that thought away, and

looked out at Young

Trees sprinting, the merry children spilling

out of their homes*, but after the airport’s*

security check, standing a few yards

away, I looked again at her, wan, pale

as a late winter’s moon and felt that old

familiar ache, my childhood’s fear,

but all I said was, see you soon, Amma,

all I did was smile and smile and

smile......


Solution 1:

From ThoughCo:

A transferred epithet is a little known—but often used—figure of speech in which a modifier (usually an adjective) qualifies a noun other than the person or thing it is actually describing. In other words, the modifier or epithet is transferred from the noun it is meant to describe to another noun in the sentence. An example of a transferred epithet is: "I had a wonderful day." The day is not in itself wonderful. The speaker had a wonderful day. The epithet "wonderful" actually describes the kind of day the speaker experienced. Some other examples of transferred epithets are "cruel bars," "sleepless night," and "suicidal sky."

The metaphor is the figurative use of "spilling" - as if the children were being tipped out like liquid.