Ed25519 uses a composite order Elliptic Curve (with a cofactor $8$) The algorithm however in the prime order subgroup of the main group. The signing operation should be using a generator/Base Point from the prime order subgroup.
There are the parameters
Order of the curve is $8.q$ where $q$ is a large prime.
$a$ = scalar/pvt key
$B$ = base point, generator of the prime order subgroup
$A = a.B$ = public key /verification key
In the signing process, a secret nonce $r$ is generated deterministically.
Then, $R = rB$
$k = Hash(R + A + M) \bmod q$
$s = r + ka \bmod q$
and $\lbrace R, s \rbrace$ is output as the signature.
The verification process however depends a check which is different between batched & unbatched verification.
As per this blog,
Batched verification uses a cofactored formula
$R =  ([s]B−[k]A) $
Unbatched uses a cofactorless formula
The original blog explains why batched verification will verify even if you use non-torsion safe cofactor clearing while unbatched will verify only if you use a torsion-safe cofactor clearing.
This Q & A from CryptoSE explains the difference & why cofactored is better.
This preprint also says the following
We claim that only cofactored verifica-tions, single and batch, are compatible with each other 4. Other combinations (cofactorless-single with cofactorless-batch; cofactorless-signle with cofactored-batch; cofactored-single with cofactorless-batch) are all incompatible.
I can understand the other differences between batched & unbatched verification (batch optimizations can be done). However, why don't both batched & unbatched both use cofactored verification?