Does 1 Timothy 4:10 mean all people are saved whether they believe in the Lord or not?

"We struggle and work hard, because we have placed our hope in the living God, who is the Savior of all and especially of those who believe." (1 Tim. 4:10)

My question is the meaning of "...Savior of all and especially of those who believe."
Update: Everyone said almost the same thing that Christ is the savior of all but not all will be saved. Everyone deserves BA. Thanks for clearing this up.
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