"In general, Ophthalmology = surgery, Optometry = no surgery. "
That is not entirely true. Optometrists can do minor surgeries and in the state of OK can do Lasik.
During an interview I had, I was asked the difference and I always thought it was the way you quoted it. But the person who interviewed me told me I was wrong. The field is changing and optometrists are beginning to be able to do what ophthalmologists can do.
Also Ophthalmologists are medical healthcare professionals because they have to go to medical school while optometrists only have to go to 4 year optometry professional school.
They both can specialize in different things, like Retina and Glaucoma.
Hope that helps!