Does a thermal photon radiate spherically whereas a photon radiates in a circle/beam? How do you tell a thermal photon of, say 3 eV, from a photon of light?
All photons are excitations of the photon quantum field. The photon is actually not a great description of propagating light - it tends to be far more useful when you're considering light exchanging energy with something else.
If you insist on a photon description then you'd have to treat the radiation as a superposition of photons. A beam of light would be a superposition of photons moving in roughly the same direction, while spherical radiation would be a superposition of photons moving in all directions.
Whatever the case, all photons are excitations of the same quantum field irrespective of their source, so the simple answer to your question is no.