This paper classifies Algorithmic Traders (ATs) as Proprietary Algorithmic Traders (PATs) and Buy-side Algorithmic Traders (BATs) and examines their dynamic relationship with market quality, using data from the National Stock Exchange (NSE), India. We find that the two categories of traders cause a differential impact on market quality measures and vice versa. BATs' order placement improves liquidity by narrowing the quoted spread, while PATs' and BATs' cancellation worsens liquidity by widening the quoted spread. PATs' order placement increases the price impact but reduces the realized spread, whereas their cancellation increases the realized spread. Furthermore, when the quoted spread increases, ATs increase their order placement and cancellation. When the realized spread increases, PATs cancel less of their orders. Contrarily, when the price impact increases, PATs' participation (both order placement and cancellation) and BATs' cancellation increase. Besides, we provide new evidence that among the ATs, order placement of BATs crowds out that of PATs, but not vice versa.