By a theorem of Lazard, 1-d formal group laws over separably closed fields of char $p$ are classified up to isomorphism by their height.
Are there invariants of formal group laws other than height (and the characteristic of their underlying field) that are not isomorphism invariants?
I've been informed that if k is algebraically closed and char p, then elliptic curves are classified by the j-invariant.
Lazard's theorem says that their associated FormalGrpLaws are isomorphic to the unique 1-dimensional FormalGrpLaw of height 1 or of height 2 (the Honda formal group law).
So there are certainly more EllipticCurve/k than FormalGrpLaw/k!
Besides, say, distinguishing between a singular and supersingular elliptic curve, what properties of the original group scheme $G \to \text{Spec} R$ are recoverable after choosing a concrete isomorphism $G \simeq \text{Spf }R[[t]]$?