A strategic heavy cruiser was a Starfleet designation for large powerful long-range cruisers. These cruisers were heavily armed and armoured. So to attack priority targets behind enemy lines with little to any escorts.
The term strategic heavy cruiser was a Starfleet euphemism for a battle cruiser. The initial design requirements from Starfleet were for these vessels to have their offensive armament based around the use of pulse phasers. Which were successfully introduced on the smaller Defiant-class heavy escorts. (DS9 video game: Dominion Wars)