There is no difference between the belief the devils have and belief only that many have today.
Many today, just like the devils, believe "mental assent" that "there is one God" and they also may even believe in the existence and historical facts about Christ, but they
DO NOT believe/entrust their spiritual well being to Christ; have faith/reliance upon Christ for salvation.
The devil's belief is, as you say, a mere mental assent of the mind and contains no obedient works.
Their mental assent belief does not produce obedient works because
their trust and reliance is in Satan, NOT IN CHRIST, as demonstrated by their rebellion in heaven and continuous evil works. You are not getting to the root of the issue.
Belief only, as many have today, is likewise a mere mental assent, a belief that contains no obedient work.
If someone
says/claims he has faith but he has
no works to back up his claim (James 2:14-16) then he does not have genuine faith but an
empty profession of faith, a dead faith. Many professing Christians today have "mere mental assent belief" in Christ and their trust and reliance is in works for salvation. That is not saving faith. Attempted so called good works conjured up through the flesh in an effort to be saved by works is not obedient work. Just look at the Pharisees.
You posted "The word "believe" can describe mere mental assent belief, as in (James 2:19) or also include trust and reliance in Christ for salvation, as in (Acts 16:31)."
Amen!
trust and reliance on Christ"?
It means your trust and reliance is exclusively in Christ for salvation and you are not trusting and relying on your works to save you. Again, the word translated faith is found in the Greek lexicon of the Strong’s Exhaustive Concordance and is defined as follows: #4102; pistis; persuasion, i.e. credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher),
especially reliance upon Christ for salvation; abstractly, constancy in such profession; by extension, the system of religious (Gospel) truth itself:--assurance, belief, believe, faith, fidelity. The word translated believe is from the greek word pisteuō which means "to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to
entrust (especially one’s spiritual well being to Christ)."
trust and reliance" an obedient work of belief in doing what Christ said, Lk 6:46
Faith/belief is trust and reliance in Jesus Christ for salvation. Doing what Jesus says afterwards is works. Faith is the root and works are the fruit of salvation. If you are trying to save yourself by works, then you are not doing what Christ said. Neither were the Pharisees. You can't seem to make a distinction between faith and works. To you, faith "is" multiple acts of obedience, faith "is" works. Faith "is" the substance of things hoped for, the evidence of things not seen. Multiple acts of obedience which follow are works and we are not saved by works but through faith in Christ.
or
is "trust and reliance" just mental thoughts, mental acknowledgements, mental assent of the mind where the believer does no works but just has "mental acknowledgments" of some information for Christ has done all the work?
Those whose trust and reliance is in Christ for salvation have been made alive together with Christ by grace through faith and created in Christ Jesus unto/for good works (Ephesians 2:8-10). Trust and reliance in Christ for salvation results in a new creation in Christ and producing good works BECAUSE we are saved, not to become saved. Doing no works is not the fruit of salvation, but the fruit of unbelief.
What is the difference between the chief rules belief (Jn 12:42) and the devils belief? None, for the chief rulers belief did not contain obedient works just as the devils belief.
In John 12:42, we do not know the real condition of these "believing" rulers' hearts (mere mental assent belief James 2:19) or (trust and reliance saving belief John 3:16), but we do know that they loved men's praises (v. 43) more than God's (Jn. 5:44). The Does the unwillingness of the chief rulers to confess Christ in this isolated situation throw doubt on the complete genuineness of their faith? Or did they simply have a weak moment in this isolated situation in front of the Pharisees? Does this mean they did not confess Christ to others? The Apostle Peter at one point failed to confess Jesus before men (John 18:17-27), but after the Holy Spirit was given, he was a different man who boldly confessed Him (Acts 4:8-13). We know that Peter was saved even though he had a weak moment and the same may be true for these chief rulers as well. Does the text specifically say that they were saved or not saved? If the chief rulers truly believed (trusted in Christ for salvation) even though they had a weak moment, then they are saved (John 3:16). If their lack of confession was the result of a lack of genuine belief, then they are not saved (John 3:18).
What is the difference between your belief and the devils belief? You both believe "mental assent" that "there is one God" and you both believe "mental assent" in the existence and historical facts about Christ. Neither of you are trusting exclusively in Jesus Christ for salvation. Their trust and reliance is in Satan, as demonstrated by their rebellion in heaven and continuous evil works and your trust and reliance is in water and works, as demonstrated by you promoting your works based false gospel and continuous self righteous works.
There are many people that say their belief is "trust and reliance on Christ" for salvation, yet they all belong to many religious organizations that believe things totally contradictory to each other. Will they all be saved believing things contradictory to each other even though they all claim to have a belief is "trust and reliance on Christ"?
Not everyone who claims to be a genuine Christian really is. In Matthew 7:21, Jesus said - "Not everyone who says to Me, 'Lord, Lord,' shall enter the kingdom of heaven, but he who does the
will of My Father in heaven. 22 Many will say to me in that day, Lord, Lord, have we not
prophesied in thy name? and in thy name have
cast out devils? and in thy name done
many wonderful works. NOTICE THEY ARE TRUSTING IN THEIR WORKS FOR SALVATION. in John 6:40, Jesus said - For my Father's
will is that everyone who looks to the Son and
believes in him shall have eternal life, and I will raise him up at the last day. NOTICE BELIEVES IN HIM, NOT IN WORKS, AS THESE MANY PEOPLE IN VERSE 22 DO. BELIEVES IN HIM/FAITH IN CHRIST (AND NOT SALVATION BY WORKS) IS THE WILL OF THE FATHER.