There is no a definite answer.
On one hand, there are spells that specifically says they create magical darkness in its effect, or at least make any mention of it, but contain no reference to the Darkness spell or to shadowy illumination.
Black Sand (sandstorm splat book, page 112):
This spell creates an area of black sand [...] A region of black sand
literally swallows light, emitting magical darkness rising to a height
of 20 feet over the surface.
Assassin's Darkness (Complete Scoundrel, page 95):
You call a globe of absolute darkness into being, which only you can
see through [...]
Even creatures that have darkvision cannot see through this magical
obscurement, although creatures capable of seeing in magical darkness
(such as devils) are not affected by it.
Scattergloom (Dragons of Faerûn, page 118)
You create four cylinders of magical darkness within the area, which
randomly and rapidly move around at ground level, giving concealment
to nearby creatures.
Control Darkness and Shadow(Champions of Ruin, page 29)
Normal shadows now grant a +4 bonus on Hide checks and provide
concealment to creatures within them. Magical darkness now confers
total concealment to anyone within its area.
On the other hand, there is a bunch of spells that say nothing about shadowy illumination, but that reference the Darkness spell, like Deeper Darkness or Ravenous Darkness (Complete Champion, page 126), so we can assume that those do provide shadowy illumination.
I have searched a concrete definition of Magical darkness , but I am unable to find one. I am also unable to find a common trend to all spells that mention the term, and that imply that the effect of the spells that create magical darkness always include shadowy illumination. Some spells create shadowy illumination (darkness spell and equivalents) which is a mundane light condition described here , which gives concealment, with some magical side effects that vary with the spell. Other spell create conditions more akin to darkness (those inside are blinded and/or receive full concealment) but they do not establish a clear equivalence between magical darkness and mundane darkness.
That said, my books are not exactly the latest editions and I may have missed any errata, dragon magazine article or something that could clarify this a little more. Also, nomenclature in 3.5 material can be a bit inconsistent and confusing sometimes. In conclusion, there is no absolute proof in favour or against the premise in the OP question.