1) Hello, my name is Emily and I am an artist who draws [x.]
That is how to say this in English.
He is an artist who draws, paints and sculpts the Native American Indian in a rustic impressionistic style.
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2) Hello, my name is Emily and I do drawings of [whatever].
The obvious crowd pleaser in the show is The Great Travelling Art Exhibition by British artist Ben Long’s DVD of his drawings in the dust on the backs of delivery vans parked in the car park at Covent Garden Markets in London. He does drawings of horses, little girls with puppy dogs, blue finches, Spitfire fighters – all the kinds of things people like to see done in well executed drawings.
The word artist in English can be further qualified. There is no good word for a person who only draws (pencil or charcoal) pictures of stuff.
Even languages that have words like dessinateur or dibujante, French and Spanish respectively, require clarification in context. It is not obvious on their face that these words refer to art(istic) drawing.
So, English is not the only language that doesn't have a good noun for the person who does drawings. And I don't think it's worth belaboring this point further.
However, please note this description of who was probably the greatest artist of all times: Michelangelo. Below is a review of a show of his drawings. They say draftsman and designer but also artist collocated with the word drawing.
Here is one art journal (from Boston University) describes the MET show of his works:
The Metropolitan Museum of Art’s wide-ranging exhibition
“Michelangelo: Divine Draftsman & Designer” examines the artistic
production and development of the Renaissance master through his
drawings. The exhibit is a result of the recent scholarly interest in
drawings and their importance within the artistic process. [...] 200
works of art in diverse media: sculpture, paintings, architectural
models, and drawings. On view are 133 drawings by Michelangelo, from
fifty public and private collections in the United States and Europe,
including studies of anatomy, preparatory sketches, as well as highly
finished compositions. The exhibition celebrates Michelangelo as a
disegnatore, draftsman, and demonstrates his extensive use of disegno, drawing, from his early days in Florence until his death in Rome.
Through his drawings, the exhibition effectively displays Michelangelo’s versatility as an artist as the works relate to all the artistic fields in which he was active. Beyond that, the exhibit
shows him not as a solitary artist, but rather as one operating
within a greater artistic network of patrons and artists.
draftsman and designer