There are actually two kinds of magic in Tolkien, but unfortunately he uses the word "magic" for both, which can lead to some confusion. In Letter 155 he distinguishes them:
for the purposes of the tale, some would say that there is a latent distinction such as once was called the distinction between magia and goeteia
And goes on to provide the following illustrative passage:
The Enemy's operations are by no means all goetic deceits but 'magic' that produces real effects in the physical world. But his magia he uses to bulldoze both people and things, and his goeteia to terrify and subjugate. Their magia the Elves and Gandalf use (sparingly): a magia, producing real results (like fire in a wet faggot) for specific beneficent purposes. Their goetic effects are entirely artistic and not intended to deceive: they never deceive Elves (but may deceive or bewilder unaware Men) since the difference is to them as clear as the difference to us between fiction, painting, and sculpture, and 'life'.
When people speak of magic in Middle-earth being "subtle", "low-key", "artistic", etc, it is actually the goeteia that they are talking about, but magia does exist and is used: Gandalf's lightning bolts and ignition of flammable objects, his "Word of Command", Glorfindel's unveiling at the Ford of Bruinen, and so on, even including the Fellowship's collection of magic items.
There's no evidence to suggest Force-like "action at a distance" that I'm aware of, but based on the above passage one might speculate that if it were possible, Sauron would use it for destruction and as a weapon, whereas the Elves and Gandalf would use it more constructively and positively, or for defence.
The only magical duel that Tolkien described in any real detail was that between Finrod Felagund and Sauron in the Silmarillion, and I'll quote it in full because it's a good example of the way these things work in Tolkien:
Thus befell the contest of Sauron and Felagund which is renowned. For Felagund strove with Sauron in songs of power, and the power of the King was very great; but Sauron had the mastery, as is told in the Lay of Leithian:
He chanted a song of wizardry,
Of piercing, opening, of treachery,
Revealing, uncovering, betraying.
Then sudden Felagund there swaying,
Sang in a song of staying,
Resisting, battling against power,
Of secrets kept, strength like a tower,
And trust unbroken, freedom, escape;
Of changing and shifting shape,
Of snares eluded, broken traps,
The prison opening, the chain that snaps.
Backwards and forwards swayed their song.
Reeling foundering, as ever more strong
The chanting swelled, Felagund fought,
And all the magic and might he brought
Of Elvenesse into his words.
Softly in the gloom they heard the birds
Singing afar in Nargothrond,
The sighing of the Sea beyond,
Beyond the western world, on sand,
On sand of pearls on Elvenland.
Then in the doom gathered; darkness growing
In Valinor, the red blood flowing
Beside the Sea, where the Noldor slew
The Foamriders, and stealing drew
Their white ships with their white sails
From lamplit havens.
The wind wails,
The wolf howls.
The ravens flee.
The ice mutters in the mouths of the Sea.
The captives sad in Angband mourn.
Thunder rumbles, the fires burn-
And Finrod fell before the throne.
This supports the speculation I made above: note that Sauron uses his song offensively whereas Finrod is primarily defensive.