"Finish" and "end" have similar meanings,
and are often interchangeable. There are some differences, though.
According to Michael Swan*.
1. 'finish' + object:
When we talk about getting to the end of something or completing an activity, we usually prefer 'finish'.
He never lets me finish a sentence.
She's always starting something new, but she never finishes anything.
You'll never finish that hamburger – it's too big for you.
Have you finished cleaning the floor yet?
Note that 'finish' can be followed by an –ing form [but 'end' is not followed by an –ing form].
2. 'end' + object:
When we talk about stopping or breaking something off, we usually prefer 'end.:
I decided it was time to end our affair
It's time to end the uncertainty – the Prime Minister must speak out.
'End' cannot be followed by an –ing form:
I decided to stop seeing here (NOT …to end seeing her.)
3. 'end' + object = 'bring to a close'
When
we are talking about a special way of bringing something to a close of
'shaping the end of something, we usually prefer 'end'
How do you end a letter to somebody you don't know?
She ended her concert with three songs by Schubert.
My father ended his days (=died) in a mental hospital.
4. shape:When we are referring to the shape of things, rather than to time, we normally use 'end.'
The road ended in a building site (NOT The road finished…)
Nouns that end in –s have plurals in –es…."
5. changes: End is more common when there is an important change.
I decided it was time to end our affair.
It’s time to end the uncertainty – the Prime Minister must speak out.
The Second World War ended in 1945
source: www.english-test.net