Does a lightbulb glow due to the interaction with electromagnetic waves or due to the interaction between its atoms and the moving electrons? Today I learned that energy is transferred to a lightbulb through electromagnetic waves produced by the movement of electrons and according to Poynting's law, the direction of this energy is perpendicular to the electric field.
On the other hand, from what I previously know, light is produced due to the interaction between the light bulb's atoms and the moving electrons which means energy is carried by the moving electrons and not by the electromagnetic waves produced by the electrons.
I'm new to the this subject, so I'm confused. Does the electromagnetic waves turn on the light bulb or the moving electrons in the wires?
 A: The free electrons are given energy (over and above their random thermal energy) by an electric field propagating as a wave. That's why they get this extra energy almost simultaneously throughout the light bulb's filament when you close the switch. This extra energy is shared with atoms (or ions) of the filament through collisions between the electrons and the (vibrating) atoms. So the filament gets hot.
I think that the confusing word in your question is "carried". I would say that the energy is carried by e-m waves but given to free electrons and thence to the filament itself as thermal energy.
A: You are confusing two different electromagnetic waves
which are involved here. So I will elaborate in a more
detailed way.

*

*The cables between the power plant in your province and
the light bulb in your home are surrounded by an electromagnetic
field of low frequency ($50$ or $60$ Hz, depending on your country).
It is the Poynting vector of this low-frequency electromagnetic
field which delivers energy into the filament of the light bulb
(the blue arrows in the image below).

image based on the one from Poynting vectors of DC
circuit, showing the electric field (read arrows), magnetic
field (green arrows) and Poynting vector (blue arrows)

*Due to this electromagnetic field the electrons inside the filament
move back and forth (with frequency $50$ Hz).
When moving they collide with the metal atoms,
thus transferring kinetic energy to the atoms,
so that their unordered movement will increase.
I.e. the temperature rises very much ($\approx 2400 °$C).

*According to this temperature the filament emits
electromagnetic radiation with a broad range of very high
frequencies (roughly from $10^{14}$ to $10^{15}$ Hz), i.e. infrared and visible light.
See also Black-body radiation for the physics behind that.


so I'm confused , does the electromagnetic waves turn on the
light bulb or the moving electrons in the wires ?

As seen above it is both: The low-frequency electromagnetic waves
turns on the electrons in the light bulb. And the moving electrons
in the filament turn on the light waves.
A: The light bulb glows due to a multi-stage process of energy conversion:

*

*magnetic to electric: in the turbines/generators of the power plant, a magnetic field is converted to an electric field in a coil due to induction (well, the voltage in the power plant could also be photovoltaic, but let's consider the probability of that origin a lot lower as of today)

*electric to kinetic: as soon as you close the light switch, the electric field accelerates electrons relative to atom bodies in the circuit wires all the way from the power plant, through the light bulb, and back to the power plant; since this cannot happen faster than light, this is conveyed by electromagnetic waves, and since the electrons cannot sustain a high velocity (see stage 3), the involved electromagnetic energy may be considerable in comparison to the kinetic energy of the electrons

*kinetic to thermal: the accelerated electrons collide again with atom bodies after what is called the mean free path length; thereby, their directed kinetic energy (current) is converted into the undirected motion of the atoms (heat); since the resistance in the light bulb's wire is higher than in the public electricity network, this conversion preferably happens in the bulb

*thermal to electromagnetic: the undirected motion of the atoms of the bulb causes the electrons to wiggle so irregular and fast that they emit what is called (in idealization) black-body radiation, a mixture of all sorts of frequencies (i.e., colors), which is clustered around a certain frequency; the position of this distribution of light colors in the electromagnetic frequency spectrum is determined by the temperature of the light bulb's wire, which is why it is called the color temperature of the emitted light; the higher the temperature, the higher the most weighted frequency of the radiation; if the temperature is below I think ~400 °C you will not see the radiation because it is in the invisible infrared; if the temperature could get above 5800 °C, the emitted light would be more blue than the natural sunlight (but of course above 5800 °C even tungsten wires start to evaporate, so that it is technically not possible to get a lightbulb emit bluish light)

At any stage, there is an input energy form, an output energy form, and something that does the conversion (a technical device, part, etc.). In the last stage, the input is heat, the output is an electromagnetic field, and the wire is the converter.
