In broad strokes...
A constitution is what establishes (constitutes) the fundamental system of governance for a given state. It sets out the structure of governance, allocates certain basic powers to essential offices, defines basic rights, and the like. Constitutional powers are those written into that basic system of governance.
Statutes are laws written by legislative bodies (bodies established by the constitution, or by local communities for smaller jurisdictions). Statutes can be just about anything, but are generally constrained by the principles set out in the constitution.
A constitutional power, thus, is something inherent to the office, while a statutory power is granted after-the-fact through legislation. Statutory powers can be removed, amended, or expanded by subsequent legislation, or in many cases by the court system. Constitutional powers are more 'set in stone'; they cannot be altered without constitutional amendments, though the court system can generally place limits on their use and application.
Under the two provisions you've offered above:
The President can issue pardons, amnesties, and commutations according
The President can only exercise statutory powers with the permission
of the Cabinet.
The President would have a blanket constitutional power to issue pardons, amnesties, and commutations, but Congress would have the capacity to pass statutes specifying or limiting the exercise of that power. The upshot would likely be a series of legal tests: cases where Congress passes a specification or limitation statute, and the President sues on the grounds that Congress is infringing on the Office's constitutionally established powers. The Court's ruling in the case would effectively interpret the constitution to mean that the President's Constitutional power has specific limits, but would not reduce that constitutional power to a statutory power.