demonstrating the difference for async case:

    import contextlib
    import trio
    
    async def background():
        assert False
    
    async def main1():
        async with trio.open_nursery() as nursery:
            nursery.start_soon(background)
            await trio.sleep_forever()
    
    async def main2():
        async with contextlib.AsyncExitStack() as stack:
            nursery = await stack.enter_async_context(trio.open_nursery())
            nursery.start_soon(background)
            await trio.sleep_forever()
    
    try:
        trio.run(main1)
    except BaseException as e:
        print('main1, context:', e.__context__)
    
    try:
        trio.run(main2)
    except BaseException as e:
        print('main2, context:', e.__context__)


----
main1, context: None
main2, context: Cancelled