Await can just catch OperationCanceledException, regardless of how the cancellation was done.

UnitTests.cs

using System;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.VisualStudio.TestTools.UnitTesting;

[TestClass]
public class AwaitCanJustCatchOperationCanceledException
{
    [TestMethod]
    public async Task CancellationTokenPassedToStartNew_CanTreatAsOperationCanceledException()
    {
        var cts = new CancellationTokenSource();
        try
        {
            cts.Cancel();
            await Task.Factory.StartNew(() => { }, cts.Token);
            Assert.Fail("await was expected to throw OperationCanceledException.");
        }
        catch (OperationCanceledException ex)
        {
            Assert.AreEqual(cts.Token, ex.CancellationToken);
        }
    }

    [TestMethod]
    public async Task CancellationTokenObservedByDelegate_CanTreatAsOperationCanceledException()
    {
        var cts = new CancellationTokenSource();
        try
        {
            cts.Cancel();
            await Task.Factory.StartNew(() => { cts.Token.ThrowIfCancellationRequested(); });
            Assert.Fail("await was expected to throw OperationCanceledException.");
        }
        catch (OperationCanceledException ex)
        {
            Assert.AreEqual(cts.Token, ex.CancellationToken);
        }
    }

    [TestMethod]
    public async Task CancellationTokenObservedAndPassed_CanTreatAsOperationCanceledException()
    {
        var cts = new CancellationTokenSource();
        try
        {
            var task = Task.Factory.StartNew(() => { while (true) cts.Token.ThrowIfCancellationRequested(); }, cts.Token);
            while (task.Status != TaskStatus.Running)
                ;
            cts.Cancel();
            await task;
            Assert.Fail("await was expected to throw OperationCanceledException.");
       }
        catch (OperationCanceledException ex)
        {
            Assert.AreEqual(cts.Token, ex.CancellationToken);
        }
    }
}