Which one of the following sentences is standard English?
Two-thirds of them have their own homes.
Two-thirds of them own their homes.
As @Michael Harvey has noted, it should be two-thirds not two-third. Third is plural since their are more than one of them.
With the correction of Two-third to Two-thirds, both are standard English. They are not synonymous though.
The first could mean a number of things depending on the context, including for example:
that they have a home to live in that they don't share,
that they have a home to live in that they don't own, or
that they have a home that they own.
There may be other ways to interpret that as well.
The second makes clear that their home is owned by them.