The issue with varying fruit size/shape is likely due to an environmental factor, but we are checking with some vegetable specialists to confirm which may be the culprit (fluctuations in soil moisture, for example, or perhaps just high heat stress). Do you know what cultivar you are growing?

You are correct that fruits with a pronounced taper are due to poor or incomplete pollination, which could be due to too few pollinating insects around or active at the time the flowers were open, or due to high heat having killed some pollen.

Miri

The specialist who responded thus far says that the short cucumbers are definitely pickling cucumbers, and the whiter-skinned fruits are not being picked early enough and are getting too mature, since pickling cucumbers should be harvested comparatively small (short). The other cucumber pictured next to the pickling type is a slicing cucumber, which should not be growing on the same plant since they are definitely different cultivars. (Perhaps two seedlings that were supposed to be the same variety but were not were included in one pot when the transplant was purchased? Some nurseries starting vegetable seeds may be putting two in one pot in case one seedling doesn't make it.)

Miri

Thanks, Miri. That's interesting about the possibility of the nursery putting two seedlings together. I also realized that it's possible that what I think is one plant is actually two side by side and I can't tell...I did lose track of where I planted one of the seedlings! 

You're welcome!