Basically when a gas gets in the alveoli, it goes across the alveolar membrane into the capillaries down it's concentration gradient. The key thing here is the gradient: if there is no gradient, it won't go across.
1. Perfusion limited- let's use N2O to illustrate. When blood comes by the alveoli, there is pretty much no N2O in it, so there is a huge gradient and N2O goes across into the capillary. However, after all that N2O rushes across, there is soon equilibration between the concentration of N2O in alveolar gas and in the capillaries, so there is no gradient. The only way more N2O can get across is if a fresh supply of blood with low N2O comes by and generates a gradient, hence the term "perfusion limited" (perfusion basically means blood coming in, so the gas getting across the membrane is limited by whether new blood comes in).
2. Diffusion limited is a little easier- it's simply limited by whether or not the gas can get across the alveolar membrane into the capillary (like if the membrane is fibrotic and stiff and it can't get across, it's diffusion limited). Classic example is CO. So, as I mentioned before, gradient is key so since the capillary blood doesn't have any CO in it and the alveoli have a lot of CO (presumably from smoke inhalation or whatever), CO goes down it's concentration gradient into the capillary. Now here is the kicker: once CO gets into the capillary, it binds tightly to hemoglobin, so the amount of free CO in the blood doesn't change much, hence no equilibration and you still have a large concentration gradient even after you've inhaled a ton of CO. So as long as the membrane allows diffusion, CO will continue to go into the blood, even when the patient has cherry red mucus membranes and is keeled over, the only way CO will stop going into the blood is if it can't diffuse across membrane anymore, hence "diffusion limited".
O2 is an interesting one- it can be either perfusion or diffusion limited. In a normal healthy lung, O2 is perfusion limited because you generally breathe in enough O2 for equilibration to occur. However, in a diseased lung like emphysema, these folks don't get enough O2 across to equilibrate the amount in the blood to the amount in the alveoli, so it's basically limited by the amount they are able to get across the damaged membranes, hence diffusion limited.