All nanoparticles are nanomaterials, but not all nanomaterials are nanoparticles.
Nanoparticles are particles within a nanometer size range. Typically this is in the 10 - 999nm range, with things at the lower end being large molecules or macromolecules (such as many proteins) and at the larger end becoming microparticles (1000 - 100,000 nanometers, or 1 - 100 micrometers / um).
Nanomaterials can have broad definitions. For instance, if you have knowledge of the packing structure of different atoms comprising some form of a metal alloy, you are gaining insight into the structure of the metal at the nanomaterials level.
Another example of nanomaterials that are not nanoparticles is transistors and most of your computer’s hardware. Each transistor is on the order of ~10 nanometers, but it is not a nanoparticle (someone may argue this point :) ).
Nanoparticles can be biological, such as those used for gene or drug delivery applications in FDA/clinical applications, or non-biological such as the titanium and zinc nanoparticles in some sunblocks. They can be made of metals, proteins, genes, ceramics, or any range of materials that are normally found in the world. However, they are constrained to being in a particle format within certain size ranges as opposed to being a more solid matrix with some form of nanostructure (nanomaterials).
You can, also, include nanoparticles within solid matrixes such as ceramics and buildings to modulate their properties.
Carbon nanotubes *can* be used to make nanoparticles. Nanoparticles can be spherical, oblong, tube-like, or any shape you can imagine. However, carbon nanotubes are very, very thin. Depending on whether they are single-, double- or multi-walled, their thickness can range from 2 - 9.5nm (Single, Double, MultiWall Carbon Nanotube Properties & Applications). An aggregate of carbon nanotubes or a 9.5nm x 50nm carbon nanotube would be considered a nanoparticle.
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