There are many synonyms for the term "fire extinguishing systems" that can describe the various types of equipment used to contain and put out fires. Some common phrases include "fire suppression systems," which are designed to quickly douse flames before they spread, and "fire sprinkler systems," which use water to extinguish or slow the progress of a fire. Other options include "fire suppression equipment," "firefighting apparatus," and "fire safety systems." Ultimately, the right term will depend on the specific context and type of system being referred to, but each of these synonyms captures the importance and urgency of containing fires swiftly and effectively.