Is this excerpt from "A Birthday" by Christina Rossetti an example of a simile, a metaphor, or an analogy?

My heart is like a singing bird
Whose nest is in a water'd shoot;
My heart is like an apple-tree
Whose boughs are bent with thick-set fruit
It is a metaphor because it compares two dissimilar entities.
It is a simile because it reflects a direct comparison between two things.
It is an analogy because it emphasizes the understated similarity.
It is an analogy because it compares two pairs of corresponding elements of two things.

Question

Is this excerpt from "A Birthday" by Christina Rossetti an example of a simile, a metaphor, or an analogy? 

My heart is like a singing bird
Whose nest is in a water'd shoot;
My heart is like an apple-tree
Whose boughs are bent with thick-set fruit
It is a metaphor because it compares two dissimilar entities.
It is a simile because it reflects a direct comparison between two things.
It is an analogy because it emphasizes the understated similarity.
It is an analogy because it compares two pairs of corresponding elements of two things.

xmoses1 · Answer

$ \sf\large\color{blue} {Welcome~to~Openstudy} $ @princetreygo! :)
I am not sure if you realize this or not, but you asked an English/Literature question in the Openstudy Feedback section :p Don't worry though! I have made this kind of mistake before too. If you could, please close the question and re-ask it in the proper section. Thank you, and have fun asking and answering on Openstudy! :)