So fundamentally in warfare, per Citino, there are two types of warfare - the war of manoeuvre and the war of material.
The war of manoeuvre seeks to defeat the enemy without wearing them down first, because wearing down the enemy is costly to both sides; the war of material seeks to defeat the enemy by wearing them down, because their side is more able to endure the process.
Now, within the war of materiel there's the subsets of trying to win with equipment or with manpower, and of course there's more nuance to it.
I would characterize the generals in the East who got close to taking Richmond, or who had to defend it, as follows:
Lee - fundamentally engaged in attempting to fight a war of manoeuvre first. His state was the weaker in resource terms and he wanted to destroy an enemy army without having to wear them down because his own resources could not sustain such a conflict for as long.
McClellan - fundamentally engaged in attempting to fight a war of equipment first and manoeuvre second. His operations were predicated on using manoeuvre where possible, and he's certainly willing to attack where needed, but his end-game for the Richmond operations (and the Yorktown operations, when required) was based on the use of his artillery superiority to create a situation where the Confederates had to attack at heavy cost into his entrenchments - or face bombardment and abandon Richmond.
Grant - fundamentally engaged in attempting to fight a war of manpower first and manoeuvre second. His operations certainly include manoeuvres, but they don't really involve part of the main army operating independently, and his instinct on multiple occasions when reaching Lee's dug-in lines is not to manoeuvre first - it's to hit Lee with the biggest hammer blow he can muster, and on multiple occasions he sends for more troops to get a bigger hammer.
This is not to say that Grant making this decision is incorrect, per se. Lee's army is certainly smaller than his own and is vulnerable to attrition. But we should recognize that:
If Grant was aiming to manoeuvre around Lee and get in a position to besiege Richmond, then his heavy attacks were bad decisions.
If Grant was aiming to beat Lee in a single battle in the field, then he failed to do so.
If Grant was aiming to manoeuvre around Lee and cut him off from Richmond, then he failed to do so.
If Grant was aiming to beat Lee through attrition (i.e. his manoeuvres were to create a situation where the battles would cost Lee more than they cost Grant) then he failed to do so.
If Grant was mostly manoeuvering around to get in position to besiege Richmond, but made the attacks for opportunistic or political-support reasons (i.e. to "prove" that he was a tough minded general) then he was successful at maintaining that political support.