What other types of Juniper are there (scientific names) other that
chinensis and rigida (sic)?

Juniperus is a very large genus. Even if you count only those species which are
used for bonsai, there are more than you can imagine. People tend to use the
species which are most available in their area.
Juniperus procumbens 'Nana' is widely sold for bonsai, but many trees labeled
that are actually J. squamata.
In the US, we use J. virginiana, J. scopulorum, J. torulosa, & a number of
other western species. Some growers in Europe use J. communis, but it has a bad
reputation for not living long in containers.

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)