The two words are the same in Hungarian: SZABADSÁG meaning ’freedom’ as in e.g. Szabadság híd (Liberty/freedom Bridge) or Szabadság szobor (Liberty Statue, see photo). The root of the word is the adjective SZABAD (free) and thus szabadság is ”free-ness”, and when you are free from work, that’s holiday: SZABADSÁG. Common phrases with the word include ”szabadságra menni” (go on holiday). In July and August you can easily come across a sign like this: SZABADSÁGOLÁSOK MIATT ZÁRVA, meaning ”Closed due to employees’ having holiday”. The word is quite tricky SZABAD+SÁG+OL+ÁS+OK (free + ness + making it a verb + ness + ’s’ plural) – literally: letting emmployees go on holiday.
The word szabad is very often used since it’s pretty multifunctional, like in the phrase SZABAD? meaning ’May I?’ or ‘Is it free?’. And you might overhear young mothers warning their children NEM SZABAD! i.e. ‘You must not do that!’.