Sequencing can be a noun or a verb and refers to the process of putting something into a sequence. Whereas sequence isn't the process but just refers to the state. For example, "the numbers are already in a sequence." (Noun) "I am sequencing the numbers." (Verb) "The sequencing of the numbers happened earlier today" (Noun)

It's just like the difference between "song" and "singing". When a singer is singing (adjective), singing (noun) is what she is doing, and the thing that she sings is a song. The verb "to sequence" means to put some things in an order. While you sequence some things, you are sequencing (adjective) them, sequencing (noun) is what you are doing, and the fruit of your labor is a sequence.