Photosynthesis allows plants to suck up CO2 and emit O2, right? Do different plants suck up different levels of CO2? If different plant species take up different amounts of CO2, what part of them allows them to do that?

Any green parts of plants are involved in photosynthesis. Usually this means the leaves, although in some plants the twigs and stems are able to photosynthesise as well. However, they use the CO2 to create sugars that can be transported anywhere in the plant. This occurs through the phloem, which is the equivalent of the bloodstream in plants, but obviously works very differently (they don't have a a heart!).

You're also correct that different plants can take up CO2 at different rates. In some cases this is because of the type of chemical pathway they use - trees, grain crops and cacti all make sugars through photosynthesis in slightly different ways. Grain crops like maize are the most efficient at taking up carbon for a given area of leaf. However, even with the same biochemical pathways, different plant species can be faster or slower.

Why aren't all species fast, you might wonder. Well, for the same reason that not all humans can run like Asafa Powell. Some of us can run quickly over short distances, some can run marathons, others (like me) are best just walking. Plants are much the same - they can't be good at everything. Cacti have slow photosynthesis because they're adapted for survival in the desert instead.