We have two type of atoms comprising most of the sun's structure. hydrogen and helium. and these have a noncontinuous spectrum.

but the sun has a continuous spectrum like a black body radiation because of free to bond or free to free radiation.
there is three type of transition:

**1. bond to bond (which is discontinuous)

2. free to bond (a free electron bond to an atom and radiate photons with continuous frequency)

3. free to free (a free electron change its speed due to interaction with a potential and radiate photons with continuous frequency)**

the last one also called Bremsstrahlung radiation.

so free electrons in the plasma medium in the sun's corona radiate Bremsstrahlung radiation due to statistical collisions and the output result is a continuous spectrum like back body radiation.

the tungsten in bulb light also behaves in this manner. electrons from electrical current collide with heavy atoms and free-free transitions occurred (Bremsstrahlung radiation) and we have a continuous light due to this interaction.

this is also true for continuous radiation of hot objects and metals.