Full Idea
If logically necessary truths are consequences of the laws of logic, then I think they are only a proper sub-class of the class of metaphysically necessary truths.
Clarification
A 'proper' sub-class must be smaller than the other class
Gist of Idea
Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities
Source
E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 1)
Book Reference
-: 'Mind' [-], p.2
A Reaction
The problem for this is unusual and bizarre systems of logic, or systems that contradict one another. This idea is only plausible if you talk about the truths derived from some roughly 'classical' core of logic. 'Tonk' won't do it!