We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time τ diverges as the packing fraction φ approaches a threshold related to percolation, while for short-lived bonds, the φ-dependence of τ is more typical of a glassy system. At intermediate bond lifetimes, the φ-dependence of τ is driven by percolation at low φ, but then crosses over to glassy behavior at higher φ. We also study the wavevector dependence of the percolation dynamics.