munter
alert
Awake, lively, and in a good mood; the opposite of tired.
Nach einer Tasse Kaffee fühlte er sich sofort viel munterer.
After a cup of coffee, he immediately felt much more alert.

lively / alert
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alert
Awake, lively, and in a good mood; the opposite of tired.
Nach einer Tasse Kaffee fühlte er sich sofort viel munterer.
After a cup of coffee, he immediately felt much more alert.

The adjective 'munter' (lively/alert) is the basis for the verb 'aufmuntern' (to cheer up). To cheer someone up means to make them happy and energetic again, in other words to make them 'munter' (lively/alert) again.
Mit einem Witz versuchte sie, ihre traurige Freundin aufzumuntern.
With a joke, she tried to cheer up her sad friend.
In the meaning of 'wach' (awake), 'munter' (alert) is often used in fixed combinations. Typical phrases are 'munter werden' (to wake up and feel fit) and 'jemanden munter machen' (to wake someone up, e.g., with coffee).
Ein Spaziergang an der frischen Luft macht oft schnell wieder munter.
A walk in the fresh air often quickly makes you feel alert again.
'Munter' (cheerful/lively) can describe not only people, but also things or activities that are cheerful and lively. For example, people speak of a 'muntere Melodie' (cheerful melody) or a 'munteres Gespräch' (lively conversation).
Aus der Küche hörte man munteres Geklapper von Töpfen und Pfannen.
From the kitchen you could hear the cheerful clattering of pots and pans.
As an adverb, 'munter' expresses that an action continues carefree and without interruption. It then stands directly with the verb, often in the combination 'munter weiter...' (to keep ... cheerfully).
Die Kinder spielten munter im Regen weiter.
The children kept playing cheerfully in the rain.
fresh
'frisch' and 'munter' can both describe someone who is not tired and has energy. 'frisch' fits especially when someone has regained strength after sleep, a break, or rest. 'munter' emphasizes more strongly that someone is awake, lively, and often in a good mood too. So a person can look 'frisch' because they are rested, and seem 'munter' because they are active and cheerful. For people, both are possible, but 'munter' sounds more lively.

Obwohl die Reise lang war, blieb das Kind den ganzen Tag munter.
Although the trip was long, the child stayed lively all day.
Nach einer kurzen Pause fühlte ich mich wieder frisch.
After a short break, I felt fresh again.