Attitude is everything when you are self employed. Some people consider it arrogance, others say it is confidence. A healthy dose of bravado can get you places that others may not even try to go.
Does it really matter if you refer to yourself as a vendor? I don't think so but there are those who feel that label is less than what they are. I don't mind and this blog talks about why.
Nothing that looks easy was to begin with. Hard work is what brings the illusion of effortlessness. This is why you work so hard, it makes it simple to do what others think is impossible.
I have so many followers who just do art for fun. Some of my students express remorse because they haven't used their materials since they attended class. There is nothing that says doing art is an obligation.
Students might be a reflection of your teaching but their accomplishments are their own. I am proud of what they do and pleased that they are doing so well.