What do you call this type of sentence? [migrated]
[1] The baby was born.
[2] The house was built.
These are both called short passives, the type of passive where a by phrase can usually be optionally omitted, cf. The house was built in 1960 (by a reputable local builder).
In your first example with "born", no by phrase would be possible, cf. *"The baby was born by a Greek peasant".
The sentence is written in passive voice.