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In my .tezos-client/secret_keys file, I have two keys of different lengths. Both start with edsk and are unencrypted.

The first is 98 characters long, which I believe is the actual secret key. The second is 54 characters long, which I believe is a seed. (Why secret key is 98 char long in tezos?).

New keys are always 54 characters long. Is it correct to interpret this as tezos-client is storing seeds in a file called 'secret_keys'? Why would tezos-client not store the full 98 character secret key?

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An ed25519 "secret key" is derived deterministically from a seed. As you point out the seed is shorter than the "secret key" which may make it more practical to work with. Both can be stored in this file.

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