'To wait', German 'warten' and Dutch 'wachten' look similar and all mean "to wait", but they have different origins.
'Warten' is not at all etymologically related to 'to wait' and 'wachten'.
'To wait' ultimately stems from the same word as 'wachten' but went through French.
Here are more related words, such as 'to watch', 'to wake', 'to guard', and 'warden':