wach
awake
Not sleeping; in a state of being awake.
Wegen des Lärms war ich die halbe Nacht wach.
Because of the noise, I was awake half the night.

awake / alert
Loading your saved state.
awake
Not sleeping; in a state of being awake.
Wegen des Lärms war ich die halbe Nacht wach.
Because of the noise, I was awake half the night.

'Wach' (awake, the state) is closely related to the verbs 'aufwachen' (to wake up, the act of becoming awake) and 'wecken' (to wake someone up). These words describe different aspects of the same concept.
Ich wache jeden Morgen um sieben Uhr auf und bin dann sofort wach.
I wake up every morning at seven and am then immediately awake.
The adjective 'wach' (awake) is very often combined with the verbs 'sein' (to be), 'bleiben' (to stay), and 'werden' (to become). 'Wach sein' describes the state, 'wach bleiben' the continuation, and 'wach werden' the transition to being awake.
Ich trinke Kaffee, um länger wach zu bleiben.
I drink coffee to stay awake longer.
In the meaning 'nicht schlafend' (not sleeping), 'wach' (awake) is almost always used predicatively, meaning it comes after the verb and describes the state of the subject.
Bist du noch wach oder schläfst du schon?
Are you still awake, or are you already sleeping?
When 'wach' (alert) means mental attentiveness, it can also stand before a noun. Typical expressions are 'ein wacher Geist' (an alert mind) or observing something 'mit wachen Augen' (with alert eyes).
Er ist ein alter Mann, hat aber immer noch einen sehr wachen Geist.
He is an old man, but he still has a very alert mind.
conscious / deliberate
'bewusst' and 'wach' can both describe that someone is not without perception. 'wach' mainly means that someone is not sleeping. It can also mean that someone is alert. 'bewusst' in this context means that someone is conscious and able to perceive their surroundings. The words can be confused after an accident or in cases of illness. In that situation, 'bewusst' is more precise when the question is whether a person can react at all. 'wach' is more suitable in everyday life when someone is not sleeping or is supposed to be alert.

Vor der Reise bin ich schon um fünf Uhr wach.
Before the trip, I am already awake at five o'clock.
Nach dem Sturz war der Mann wieder bewusst und konnte sprechen.
After the fall, the man was conscious again and could speak.