No, your understanding is wrong.
First, all surgeons are medical doctors. Secondly, all surgeons specialise in a specific discipline.
Ophthalmology is a specialty that medical doctors go into and then they further specialise into medical or surgical ophthalmology. Then, there will be further specialisation and training into specific eye pathologies.
There are no student surgeons. There are surgeons still in training - who are fully qualified medical doctors who now focus on a particular area of surgery. A previous posted was right - the “student”/“trainee” surgeon could have 7-9 years of specialised surgical ophthalmology experience.
Secondly, how NHS operations work is that you will have a named consultant responsible for your child’s care. They will then need to have an assistant who will assist by doing parts of the operation or holding instruments or providing traction - this means that they will be scrubbed, standing be the bedside and be participating throughout the operation.
This assistant (or second operator) will almost always be a “junior doctor.” Sometimes the operation will need several assistants and some simple operations require none.
I cannot comment as to how much of the operation will be performed by the “junior doctor surgeon” but it depends on so many factors - including the difficulty of the operation, the rarity of the operation, patient, how many other cases are scheduled that day, bed pressures, level of junior, level of consultant and personalities of both.
While I understand your reluctance to not have students/juniors operate on your child - this demonstrates how the public perception of NHS doctors as “juniors” is really damaging to patients. There really won’t be a spotty teenager or 21 year old let loose to operate on your child.