The most "advanced" readers will capture the MRZ (machine readable zone) and OCR the VIZ (human readable area) and compare them.
Airlines and airports are pushing to go heavily self-serve over the next few years, so new readers can also do facial matching to your identity document to check bags or print boarding passes.
An online check is superior because it can be reactive. If Jim's identical twin, Sam, steals Jim's passport, Jim can phone it in and have the online system updated so that when Sam tries to fly to another country on Jim's passport that won't work - but with just cryptography we can't solve that.
EU passports support a further level of mutual authentication in order to get the fingerprints, where the terminal is verified by the passport as well.
There is a further step called Active Authentication where the reader sends the passport random data and it signs this data with a public key that can be verified as authentic.