The smaller one, most often sold in 4-8" pots is the Spathiphyllum wallisii. It's about 1' tall. The larger one, up to 2' is Spathiphyllum 'Mauna Loa'.

I've read the lily is the flower representing peace

Although it could be that your peace lily is not receiving enough water or fertilizer, the most likely cause is that the spathe is simply aging. The spathe is actually a modified leaf and, like most leaves, goes through photosynthesis. After some time, the chlorophyll within the spathe will begin to turn green.

If you do not mind the appearance you may choose to keep the plant as is. Otherwise you may cut the stalk right above the soil line to begin making room for new growth.

The Lily is a well known flower. I believe the french chose this flower to symbolize peace in their nation.

Better music.