HOW TO DEFINE? LET'S ASK NOAA and USCS WHAT ENDANGERED, THREATENED, IMPERILED, and AT-RISK MEAN

First let's see what NOAA has to say...

OCEAN SERVICE : NOAA GOV THREATENED and ENDANGERED SPECIES

Excerpt: The ENDANGERED SPECIES ACT (ESA) defines an endangered species as "any species which is in danger of extinction throughout all or a significant portion of its range." Endangered species are automatically protected by prohibitions of several types of "take," including harming, harassing, collecting, or killing, under Section 9 of the ESA. There are some limited exceptions to these rules listed in Section 10 of the ESA. The Kemp's ridley turtle, considered the smallest marine turtle in the world, is listed as an endangered species throughout its range of the Gulf of America and entire U.S. Atlantic seaboard.

The ESA defines a threatened species as "any species which is likely to become an endangered species within the foreseeable future throughout all or a significant portion of its range." Threatened species receive protections through separate regulations issued under Section 4(d) of the ESA. These regulations occur separately from the listing and detail what take prohibitions are in effect. Also called 4(d) rules, they can include the same prohibitions under Section 9. 

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USGS : ENDANGERED, THREATENED, AT RISK SPECIES

Excerpt: Under the ENDANGERED SPECIES ACT (ESA), plant and animal species may be listed as either endangered or threatened. “Endangered” means a species is in danger of extinction throughout all or a significant portion of its range. “Threatened” means a species is likely to become endangered within the foreseeable future.

States have their own ESA-type laws, so species can have different Threatened/Endangered statuses at the federal and state levels. The USGS typically refers to the federal status unless otherwise noted.

"Imperiled" or "at risk" are not legal terms under ESA, but more biological terms. Generally speaking, they are animals and plants that are in decline and may be in danger of extinction. Those terms can include species that are at low populations and near extinction but still not legally protected under ESA.