Role of the analyzer in the completion suggester

The completion suggester is based on a field that has to be mapped with
type completion.
This has by default index- and search-analyzer set to simple, but a
different analyzer can be freely set.

After the indexing process, the input text is stored in a finite state
transducer, and suggestions are only returned on prefixes matching the
provided text.

What I'm struggling to understand is the role of the analyzer in this
whole process
. Is the analyzer only used to process the input string to
extract the string that will actually be stored in the FST? Is the search
analyzer only used to process the search text and extract the actual path
to be followed to traverse the finite state machine?

Thank you in advance,

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