When I told a yoga instructor that thoughts arise while I meditate, she replied, "You are not getting into the meditative state." So -
(i) Is there a single "meditative state"?
(ii) Does everyone who meditates aim to get into that "state"?
The answer to (ii) is definitely no. I have never practiced the Maharishi's Transcendental Meditation but I understand that practitioners, using a mantra, get into a peaceful inner state. However, zazen, "just sitting" meditation:
is awareness of natural mental states;
is not no thoughts arising;
thus, incorporates thoughts arising;
can be unpeaceful.
Therefore, the arising of thoughts is not a failure to meditate. Failure occurs neither when a thought arises nor when it continues naturally but only when it becomes deliberate. A monk said, "There will always be natural thoughts but don't add to them."
It follows that, as I had been told:
when I thought that I was failing to meditate, I was in fact meditating;
much meditation is not what we think of as meditation;
we learn from the thoughts that arise;
when we return our attention to the present moment, that moment includes not only the wall that we see and the cushion that we feel but whatever thought has arisen.