I have a decayed tooth that is infected, does it mean that i have a tooth abscess?

Not: For sure. If a pocket of the infection develops then you have an abcess.

Probably: Usually a tooth that "is infected" has an abscess. There is a small window of time when the infection might only be confined to the tooth and has not yet formed an abscess. Regardless the treatment is the same. Tooth must either be treated with a root canal or be extracted. The sooner you seek treatment the better chance of a good outcome.

Not necessarily: Any decayed tooth by definition is infected. When the infection spreads beyond the tooth to surrounding tissues, either soft tissue or bone, and pus is produced - that is an abscess.

Not necessarily: But it should be taken care of.

Dental Abscess: An abscess is a localized collection of pus. The nerve inside your tooth may become infected, and when that infection spreads to the bone and/or soft tissues, you have an abscess.

Infection: If it is infected it is abscessed as the words are synonymous. Please see your dentist and have the tooth treated as infections are not to be left untreated.