A tagger assigns annotation to any text it encounters. One interesting extension would be the development of a tagger which also marked up co-referring entities. Both types of parser are used to deal with raw text in a robust manner. An island parser allows for shallow levels of parsing where no further progress can be made. Island parsers are typically used in Information Extraction where the issue is to extract as much information as possible rather than produce a perfect parse tree.
Probablistic parsers assign probability values to every grammar rule.
This allows for the parser to take the most probably parse.