Nuts are a great source of energy, monounsaturated fats, omega 3 fatty acids, fiber, vitamin E, plant sterols and L-arginine.
Nuts in the culinary sense (which this website refers to) are considered seeds with nut-like characteristics – a fruit composed of large oily kernels and enclosed in a hard covering.
Nuts in day to day communication describe a food group with a similar characteristics and culinary usage. Nuts in the culinary sense can include legumes such as peanuts, seeds such as pine nuts, drupes such as almonds, capsules such as Brazil nuts, etc.
The definition or criteria can sometimes be harder to understand than simply becoming familiar with the list of the most common culinary nuts: almonds, Brazil nuts, cashews, chestnuts, coconuts, hazelnuts, macadamia, peanuts, pecans, pine nuts, pistachios and walnuts. (1)Steel JB, Wilson JB. Is there only one kind of edible nut? New Zealand Journal of Botany. Volume 50, Issue 1, 2012. pages 71-76. Available here.
Seeds in the diet provide us with energy, oils, fiber, protein and various minerals and vitamins.
In the culinary sense, seeds don’t have consistent definitions but rely on convention, depending how we eat them. On this website seeds are referred to dry seeds which are not considered nuts or legumes: chia seeds, hemp seeds, flaxseeds, pumpkin seeds, sesame seeds and sunflower seeds. Seeds from pomegranate are not dry so are in the fruit section of this website.

References   [ + ]

1. Steel JB, Wilson JB. Is there only one kind of edible nut? New Zealand Journal of Botany. Volume 50, Issue 1, 2012. pages 71-76. Available here.