It is not determined, and in different contexts there may be a different understanding of the phrase.
Firstly there is no consensus on the "first day of the week", Sometimes it is Sunday, sometimes it is Monday.
Secondly there is no consensus on whether the "first week" It could mean:
- Wednesday 1st to Saturday 4th. (or sunday 5th)
- Wednesday 1st to Tuesday 7th.
- Sunday 5th to Saturday 11th
- Monday 6th to Sunday 12th.
According to the conventions being used and the context.
To partly work around this there is the expression "First full week". This is either 5th to 11th or 6th to 12th (according to which first day of the week is being referred to)
And so "The third week" might mean:
- 12th — 18th
- 13th — 19th
- 15th — 21st
- 19th — 25th
- 20th — 26th
Unfortunately, not much else can be said. Sometimes this isn't a problem, because the phrase is vague enough for it not to matter (it vaguely indicates "not very early in February")
In contexts where it matters, you need to use actual dates. Ie. don't say "The goods will be delivered in the third week of February" but say "The goods will be delivered between the 19th and 25th of February". Similarly, you should say "The third Wednesday", not "the Wednesday of the third week".
Sometimes you might be able to guess, based on the prepostion used:
- Third week in February = 13th — 19th (or 12th)
- Third week of February = 15th — 21st
- Third full week in February = 20th — 26th (or 19th)
I suspect the ambiguity isn't unique to English.