Assessment

Assessment is all the documents that can prove if our students learned English. It does not only refer to the exams and homework, it can also be oral activities we do in the classroom, a story they wrote, an explanation they gave from a recording we played, and even a drawing they have to do of the description we read to them. 
Testing is when we ask our students for information we already know the answer for and they are supposed to know it too. It can be in an oral or written form.
Teaching is providing our students with information they can handle and understand (depending on their age and level of previous knowledge), and explaining it to them by dividing this information in four main skills: listening, speaking, reading, and writing.
These three concepts have to be personally related in order to make each of them possible. Without testing there would be no formal way to assess, without assessment we could never evaluate our students’ progress, strengths and difficulties, neither could we evaluate ourselves in order to see in which aspects we have to improve; and without teaching itself, we could not be able to test anybody on anything.
They depend and complement one another, they help us and our students to be better learners.