Great Question, brother.
I've became curious related your question and get this information:
According to Nourman Ali, Abd meaning is more to "Slave".
He make it clear here:
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https://www.youtube.com/watch?v=fJymQTW9cd4
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https://www.youtube.com/watch?v=LrIWIogwjKU
As I got from the Explanation, I consider that Slave is small part of Servant. That Means, If we are a slave, we are also a servant.
But If we are a Servant, It doesn't mean we are a Slave.
This means that Slave of Allah is rarest person than Allah's Servant.
As You've said, that Allah gives us
free will and also repays us eternally with Jannah. The
Free Will means that we always can choose either to be only a Servant or become a Slave.
Me myself think that Servant will be kind of doing everything Allah said in Quran.. We're doing this because we believe, and We have to do it. In daily life, maybe we still choose and think rationally about what will be good for us in this life, for each decision and activity...
However, A slave will always think of Allah (will Allah like this, Will Allah please with Me?) in each decision We make, and each activity We do.