Deuteranomaly causes difficulty distinguishing between shades where the precise amount of green is relevant (i.e., to a deuteranomalous person, pure yellow -- equal parts red and green -- would still look slightly reddish-orangish).
Protanomaly causes a similar effect with red, and also dims the dark/deep red part of the spectrum slightly.
If someone doesn't want to use the medical terms for them, better names are "green weakness" and "red weakness" since they don't carry the misleading "can't tell red and green apart" connotation.