Do man-made solar satellites all have roughly the same orientation of orbit around the sun?
I don't know of many, and no...
SOHO is in a halo orbit about the Sun Earth Lagrange 1 point. I seem to recall one satellite which was sent up over the Sun to look at the north pole with an inclination near 90 degrees.
enigma is perhaps referring to Ulysses.
In general, satellites launched into orbits other than round the Earth (or to land on, or go into orbit around, a specific planet; or leave the solar system altogether), have their orbits designed to match the scientific objectives for which they were created.
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