"Private toilet with septic tank" is a toilet facility used by only one household with a sewer line from the toilet so that the waste will go to a place that is waterproof and has a seepage channel (septic tank).
"Private toilet without septic tank" is a toilet facility used by only one household with a sewer line to another place such as a river, pool, etc. or without a sewer line but directly to the waste site.
"Public toilet/shared toilet/other" are toilets that cannot be classified as any of the above.