I'm guessing those are two different logs, possibly from two different species, right?
At least they look like two different species. Hard to identify for me. Because they were taken from a garden, they might be planted some time ago. That means they may not even be native, but exotic. So the list of possible species can hardly be narrowed down. Perhaps your neightbour remembers what species they are...?
If I have to make a guess...
I'd say the first one may be some type of poplar or willow. Not so much bowwood, I'm afraid...is the wood hard or soft? Any particular smell? Poplar can have a slight unpleasant smell.
The second one looks better, but I really can't identify it. The rings look somewhat like elm, but the bark does not.