Logos is the word. The word you hear and read with your natural [physical] eyes/ears. Rhema is the word you hear then ‘see’ with your spiritual ears/eyes.
Logos is for all. As it is for ‘the flesh’. It can be naturally understood, and used for reasoning. Rhema won’t make any sense to the natural mind.
1 COR 2:13 And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual. 14 The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned.
Now let’s examine the verses you asked about ...
John 14:10 ”Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works"
Here he is talking ‘spiritually’. A Father dwelling ‘in’ him ... is speaking? - doesn’t make sense. [naturally], Because those ‘words’ [rhema] are spoken for spiritual ears. God is speaking (and he isn’t there in person)
Where as ...
John 14:24 Whoever does not love me does not keep my words. And the word that you hear is not mine but the Father's who sent me"
The word [Logos] which you hear [with your natural ears]. Here Jesus is speaking (and he is there physically).