Allah the Exalted said: << و ألق عصاك فلما رءاها تهتز كأنها جآن ولى مدبرا ولم يعقب يا موسى لا تخف إني لا يخاف لدي المرسلون >

[Surat al-Naml:10] What is the staff that was with him? It is a staff he leans on and uses to drive his sheep; it is an ordinary staff. So its attribution to Musa (peace be upon him) is the attribution of a possession to its owner, not something specific to him that he was uniquely distinguished by. That is, this staff was not unique to him, nor was it a staff of a specific substance or the like; it was an ordinary staff.
"

And cast your staff

وَأَلْقِ عَصَاكَ

[Surat al-Naml:10] So he threw it This is also an example of concise omission, as mentioned earlier. Narratives always contain concise omission, because what is omitted is always known from the context, making its omission easy and straightforward.
Ibn Malik (may Allah have mercy on him) said in the Alfiyyah a rule that is among the most beneficial things, which he mentioned in the chapter on the subject (mubtada') and which is applicable to everything. He said:
Omitting what is known is permissible, just as
you would say to Zayd: "From where are you?"
Omitting what is known is permissible; this is a rule.
He said: " So he threw it

But when he saw it writhing

فَلَمَّا رَآهَا تَهْتَزُّ

[An-Naml 27:10]

and it moved .
However, interpreting the shaking as mere movement is questionable, because shaking is more emphatic than movement. It seems that shaking involves a type of force and agitation.
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As if it were a jinn

كَأَنَّهَا جَانٌّ

a light snake .
It was said to be a great snake, and it was said: the male of the snakes of the jinn.
In any case, this staff that was in his hand, which he threw, became a snake that shakes, moves, and agitates like a jinn. That is, a great snake.