TL;DR
Most probably the species will have a name for the light consisting of all wavelengths they can perceive, all of them fully saturated. This, respective to our standards is something we call white. For them the Sun will be just as "white" as it is for us and their star will be for us as white as the Sun is.
Atmosphere can significantly impact colours. We can perceive the colour of star at their ground level as violet while they can perceive ours as "orange" (in their terms). It may even happen that stars will be totally invisible for them on our planet and for us on theirs even though both we can see them on Earth and they will see it on their planet.
It is also possible, that they will use that very same name for the electromagnetic pulse saturated in full spectrum of electromagnetic wavelength of some range just like we do, but they may as well have some totally different name for it.
It's all just not so simple.
Full answer
How we see
To understand why we see colours we need to understand how is it possible that we actually "see". There are 3 layers responsible for that:
1. Physics (what reaches our eyes)
2. Physiology (how the light is converted into neural signals)
3. Psychology (how our brain interprets the signals that reach it)
Let's go one by one.
1. Physics
What we call light is actually an electromagnetic pulse in a certain range of wavelengths that (depending on the accuracy of definition) either humans are in general capable of perceiving through their sense of vision (a more common term) or physicians have defined as light (a scientific definition). The term light as we usually use it is the first one and all of this "light" is included in the second one (with plenty of additions).
Whenever we look at an object, what we actually see depends on the electromagnetic pulse that comes from the direction of that object (and can consist of pulse produced by the object, reflected by the object and that went through the object). I will get back to that later.
The Sun and pretty much all stars emit electromagnetic pulses that consists of the wide spectrum of wavelengths, from IR (or even radio) to X-Rays and Gamma. There are some (very small) bits missing and some of them are stronger than others but all in all you can "see" Sun if you look in "visible" light, UV, IR and other frequencies.
These are photos of the Sun taken in various frequencies (taken from this page).
For comparison, this are the spectres of other stars (as observed on the Earth - remember about the Doppler effect that shifts the frequencies, taken from space.fm)
As you can see, most wavelengths are covered which essentially means - those stars are to our eyes white.
2. Physiology
Essentially humans see through their eyes. To be more specific - those are the organs that capture light, focus it and change it into the electric signals that can be transmitted through a nerve system to a brain. 970
Let me focus on that last role of eyes. Retina of a human eye is covered with two main types of light receptors - cones and rodes. Cones are further split into three subtypes. Each of those types responds to a different range of an electromagnetic wavelength (and within the range where it reacts the strength of reaction is different).
Here is a representation how human rods and cones are sensitive to specific wavelengths (from this page):
Let me add that rods and cones cannot work at the same time. There is a simple mechanism that "turns on and off" rods when respectively there is not enough or sufficiently enough light for cones to operate. Let me just focus on cones as they are responsible for our colourful vision. When a specific area of an eye is exposed to some visible light (in common understanding - visible to us), the cones of that eye are "activated" if this light consists electromagnetic within specific wavelength. As a result it send impulses to brain. A strength of such depends on strength of the light of this wavelength and how close the wavelength is to the peak of the sensitivity are wavelength. If we look at something green, yellow and orange, in each case both M cone and L cone will be activated, but with each of the colours the strength of M cone reaction will lessen while L increase. Additionally at green colour also S cone will be slightly activated. All that brains receives are signals from those 3 cones.
Now the brain cannot verify what exactly triggered cones. It only knows that those three signals combined tell about a colour of the thing on which we're looking. If it was just a very narrow "beam" (in terms of consisted wavelengths) or the contrary - a broad one, a brain has no way to determine. As a result the same set of "results" from all three cones produce the same "colour" for the brain. 762