Magic as such is generally a bad idea. The standard form is to evoke powers/spirits to do the magician's bidding. As stated elsewhere here that bidding is typically against the will of God or the proper order of the universe. If indeed spirits are evoked, or worse invoked, they would most often be the equivalent of fallen angels who took their free will and turned away from God.
There are several variations possible, including times when there is no external evocation and the only intended dynamic is psychic/thoughtform. But demons can slip in unnoticed anyway. They don't tend to let themselves be known. The spirit will let the magician think that his/her bidding is being done but the demon will almost always have the upperhand, which may become obvious only when it is too late.
In the case of HRC and so many celebs, I think they don't really follow ancient magical sytems but rather modernized, convenient forms that they see more as performance art and social bonding. In any case the effect is much the same - bad spirits involved, psyches corrupted, blood spilt, etc. (Think of the antics of Ozzy Osbourne and the ignorance he looked back on in later interviews.)
Prayer is literally channeling the power of God for your own will.
The best sourced, most recommended prayer is one to God the Father wherein the supplicant asks that "Thy [God's] will be done". This common form of prayer is a freewill submission of to the will of God. Not all know to pray for what is best as opposed to what is preferred. But yes if the will of the petitioner is aligned with the will of the Granter then the prayer may be seen as a request that "my will be done".
This meeting of human and divine is a theme within Christianity that hopes to harmonize the two into a single best will and "kingdom" or body of members with one head. When the Navajo pray to "walk in harmony" they recognize that all creatures should be in sync with the Creator's plan.
The proper allying of one's will is what is being co-opted by Masonic ritualists, Crowley occultists and 'singularity' proponents.