There are so many focuses in the Fiber/Textile world that it would seem that there would be a clear deliniation between them all- so when you looked at something you say "That is design. That is art. And there is technology."
But textiles have a way of blurring the boundaries of these worlds (much like other craft arenas).
I, personally, received a degree in design. Design is often defined as solving a problem. For example: this is a wing back chair from the 1940's that the client would like time period appropriate fabric made for it. You must research the time period, design fabric that is appropriate to the piece of furniture and the time period, and execute (if asked to do so).
Fiber art is more along the lines of posing a question to the audience. Like a performance piece by Janine Antoni called Slumber originally performed in 1993. She slept and recorded her brain waves then would weave the image of the brain waves into cloth, producing a blanket which she would then sleep with the next evening. I am not 100% what the question is that she is posing, but, I feel that this a performance to make unique an experience that we all have everyday, to make it something her own.
And Textile technology is incredible! Fabrics have been developed that can record your body's temperature, heart rate, etc. They can light up, make sound, actively cool your body, or shape to your unique shape. This is a field where there is an integration between design and technology to produce incredible fabrics that are used in fashion, interiors and even art.
The textile artist/designer of today can literally be a multi-faceted crafter due to our access of information and materials. There is yarn available that is made from filaments of copper, which could be used to allow electricity to flow through the fabric, or to maintain its shape. There are books and articles and videos, all about how to add modern day technologies into traditional materials. And the access we have to those traditional materials, via online databases and museum archives is just breathtaking.
I try not to feel limited by what my degree says about me, but rather, feel connected in a wide expanse of artists and designers who have their feet in both arenas- absorbing all the information and ideas that are available.