Hodge,
Both are true - although you're right, it does seem confusing.
Here's why they're true.
Nymphs and streamers imitate different food stuffs. During winter, water is often very cold and clear and when fish focus on nymphs, what they are eating is often small. Part of the reason for this is many nymphs are smaller in winter because they haven't had as much time to grow. During clear water periods, fish are often selective about size and small nymphs are often closer to the actual size of what the fish are eating.
Streamers, since they imitate fish, are a different case in point. Small prey fishes are often quite large in winter having been born the previous year. By late spring and summer you've got a bunch of new young of the year beaitfish - but in the fall and winter they tend to be bigger. A trout in winter, although usually fairly inactive, will chomp a baitfish if the opportunity arises, epsecially sculpins. Streamers work year round but a lot of guys use other stuff during the warmer months when hatches are more prevalent. Streamers should be fished fairly slowly when the water is cold (below about 42 degrees F).