
versäumen
to miss
To fail to attend or reach an opportunity, appointment, or means of transport in time.
Ich habe die letzte Bahn versäumt und musste ein Taxi nehmen.
I missed the last train and had to take a taxi.
to miss / neglect
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to miss
To fail to attend or reach an opportunity, appointment, or means of transport in time.
Ich habe die letzte Bahn versäumt und musste ein Taxi nehmen.
I missed the last train and had to take a taxi.

to neglect
To fail or forget to do something that one should do.
Sie hat es versäumt, sich für den Kurs fristgerecht anzumelden.
She neglected to register for the course by the deadline.
The verb 'versäumen' (to miss / neglect) is inseparable. The prefix 'ver-' remains firmly attached to the stem 'säumen' in all sentence forms and tenses.
Er hat den Anfang des Films versäumt.
He missed the beginning of the film.
When 'versäumen' (to neglect) describes an omitted action, it is often used with an infinitive construction with 'zu'. The formal variant is 'es versäumen, etwas zu tun' (to neglect to do something).
Versäumen Sie nicht, Ihre Rechnungen pünktlich zu bezahlen.
Do not neglect to pay your bills on time.
In this meaning, 'versäumen' (to miss) is often combined with means of transport, appointments, or opportunities. Typical examples are: 'den Zug/Bus versäumen' (to miss the train/bus), 'einen Termin versäumen' (to miss an appointment), or 'eine Gelegenheit versäumen' (to miss an opportunity).
Wenn du jetzt nicht gehst, versäumst du deinen Flug.
If you don't leave now, you'll miss your flight.
'Versäumen' (to miss / neglect) belongs more to elevated or formal language. In everyday speech, the verb 'verpassen' (to miss) is often used, especially for appointments or means of transport.
Der Minister versäumte es, die Öffentlichkeit rechtzeitig zu informieren.
The minister neglected to inform the public in time.
to forget
Both verbs can refer to a required action that was not carried out. Vergessen states that the reason was that one did not think of it. Versäumen focuses more strongly on the action that was not carried out or on its consequences; forgetfulness does not have to be the cause.

Ich habe es versäumt, den Antrag rechtzeitig abzugeben.
I failed to submit the application on time.
Ich habe vergessen, den Antrag rechtzeitig abzugeben.
I forgot to submit the application on time.