Usually anyway. IIRC, Acrylic is a plastic that shatters instead of deforming. But most plastics (ABS (aka Legos), polypropylene (PP, #5 Plastic), Pete (most bottles), HDPE (aka cutting boards)) all are "plastic", as in having high plasticity.
IIRC, metals are actually more "plastic" (deform more before breaking) than erm... plastics. See iPhone aluminum bending issue for details.
"Plastics" are mostly petrochemical derived organic polymers. Properties of some, like acrylic glazing are relatively hard and brittle, others quite elastic and soft, e.g., foam rubber. Obviously modern life is utterly dependent on these materials which are employed in virtually everything we use from food to space probes.
There are good reasons to believe that production of "plastics" is among the highest and best use of petroleum resources, it's a shame we continue burning it up at a prodigious rate. Trends to find alternative energy sources would have benefit in this respect too.
The first were based on coal tar, starting around 1870-1880 IIRC. Then came bakelite, still used in cookware handles -- it has exceptionally good thermal resistance properties.
Discovery accelerated through the 1900s, 1910s, and 1920s, and exploded in the 1930s, with the number of materials about doubling IIRC.
Names started changing too -- from chemical (polypropelene, polyester, polystyrene) to brand (nylon, teflon, orlon).
I've also noted that with both coal and oil, there seems to have been an adoption and technological development cycle in which the first use was to burn the materials, and only later, by some decades, did the chemistry develop for materials based on the substrates. There's probably a lesson here.
Since plastic can stretch a large amount before breaking it absorbs more energy than a (inverse of tough) object, so it is tough.
Since it is easy to stretch inelastically, it is not hard.