There's two sides to what we call sentience.
One is self awareness - the awareness of ourselves as a distinct individual separate from others.
Two is reason - the ability to think through a problem and then apply the solution to that problem to other problems.
Many animals possess self awareness but not reason. Horses, for example, demonstrate the ability to identify and remember specific individuals, as do dogs. (A recent study showed that dogs would refuse treats from people who treated their owners badly). It's fairly simple to extrapolate from being able to tell Jane from Joe to knowing who you are. However, a horse can't apply the logic from one problem to another. They can only remember the solution to the problem they solved last time. I often talk about animals as having limited processing power. A cat, for example, is not able to work out that two paths can lead to the same place, leading to the amusing "looking for the door into summer" phenomenon so many cat owners observe.
Computers demonstrate reason, but not (as far as we can tell) self awareness. Computers can play chess well enough to beat the best human players - chess being a solid test of reason.
Now, I'm not entirely convinced by the test (it looks like simple diagnostics to me and thus a test of reason not self awareness, which computers possess). But it may have come somewhat close.
(And there are definitely non human animal species that demonstrate at least some high level "reason"...it's not a black and white line).