It depends.  People tend to be brand loyal to paint manufacturers.  While we understand this, all manufacturers have different tiers in their quality of products (good, better, best).

The “better and best” paints usually have better components for coverage, durability and color retention.  Some paints are better for high use applications (rental units, hotels, or high traffic areas).  Some paints just have a certain “feel” with application making the job run smoother.

So, this question is very difficult to answer a without more context.

With that said, we primarily use Benjamin Moore and Sherwin Williams paints, typically using their higher end products.

Yes, however this is not as simple as it may seem.

Take exterior homes for example.  Paints fade over time, and some paints degrade more than others.  We have tools with can read the paint color of an existing home, but it will only read the current condition of the paint and color.

We have obtained 5-10 different readings on a home in different spots and obtained 5 different colors from the readings.  They are all similar, but there is a difference.

Even if you have the original color and we repaint it with that color, it will look different.  It is a fresh coat of paint on the entire home with no fading.

In addition, most unpainted stucco homes have their color in the actual stucco when the stucco is applied.  Tinted stucco will look different than the same exact color painted on top of stucco.  

In regards to interior painting, condition of the paint and fading are usually the two factors affecting a color match.

A coat of paint on top of a 10 year old coat of paint will probably look a little different, even if it is the same color.  It will look better.  It will be even.  The walls will be brought to like-new condition, if possible.