Array P systems were introduced by Paun Gh. which is linking the two areas of membrane computing and picture grammars. Puzzle grammars were introduced by us for generating connected picture arrays in the two-dimensional plane, motivated by the problem of tiling the plane. On the other hand, incorporating into arrays the developmental type of generation used in the well-known biologically motivated L systems, Siromoney and Siromoney proposed a very general rectangular array generating model, called extended controlled tabled L array system (ECTLAS). In this paper we introduce two variations of the array P system, called BPG array P system and parallel array P system. The former has in the regions array objects and basic puzzle grammar rules (BPG), which are a specific kind of puzzle grammar rules. In the latter, the regions have rectangular array objects and tables of context-free rules. We examine these two types of P systems for their array generative power. Array P systems were introduced by Paun Gh. Which is linking the two areas of membrane computing and picture grammars. Puzzle grammars were introduced by us for generating connected picture arrays in the two-dimensional plane, motivated by the problem of tiling the plane. On the other hand, incorporating into the development of type of generation used in the well-known biologically motivated L systems, Siromoney and Siromoney proposed a very general rectangular array generating model, called extended controlled tabled L array system (ECTLAS). In this paper we The former has in the regions array objects and basic puzzle grammar rules (BPG), which are a specific kind of puzzle grammar rules. In the latter , the regions have rectangular array objects and tables of context-free rules. We examine these two types of P systems for their array generative power.