The main difference is that nested is much more likely to be used when one X is contained within another, "higher-level" X. Whereas an embedded X simply means an X which is within something - not necessarily another X (and in fact probably not, since if it was, we'd probably have used nested).

Thus in programming contexts we often refer to nested loops/queries (within higher-level loops/queries). But a gif graphic image within an email (as opposed to an email attachment) is an embedded image.

I'm sure you'd be understood if you referred to the nesting loop/query, but outer is the standard term (or sometimes, containing).

On tangerines and mandarins, clementines and satsumas

When discussing words used “in common practice” by a speech community comprising on the order of a billion speakers (~40% L1 + ~60% L2) distributed across the entire planet, sweeping generalities of usage are next to impossible.

Technical usage by scientists recognizes all of these things as various species and cultivars under the Citrus genus, but when they do so they use taxonomic binomials bearing little to no relationship to the words commonly used by these fruit. And even at the technical level, citrus taxonomy is confusing.

When used as a commonplace marketing term, words like tangerine and mandarin have no technical meaning, especially not one that is recognized across all corporations everywhere.

• I have seen the very same fruit marketed by one company under one name but by another company under another.
• I have seen quite different common names for them in America as in Australia, and I have seen common names shift over time.
• It is the people who live in areas where these fruit are grown who are the most likely to make fine distinctions between them, distinctions that are either lost or at least unrecognized by people who live in colder climes.
• I have seen residents of citrus-producing regions argue passionately about whether the clementine is larger, sweeter, and juicier than the mandarin, or whether the opposite relationship holds — and then when a sample specimen is presented them, each party in that dispute calls that fruit by a different name. *I have heard others argue that a mandarin must automatically “be” an orange not a tangerine because of the historic collocation mandarin orange.

Wikipedia reports in their article on the tangerine:

The name was first used for fruit coming from Tangier, Morocco, described as a mandarin variety.^[2] Under the Tanaka classification system, Citrus tangerina is considered a separate species. Under the Swingle system, tangerines are considered to be a group of mandarin (C. reticulata) varieties.^[3] While tangerines genetically resemble mandarins,^[3] the genetics are still not thoroughly studied.^{[dubious – discuss][4][5][6]} The term is currently applied to any reddish-orange mandarin[citation needed] (and, in some jurisdictions, mandarin-like hybrids, including some tangors^[7][8]), but the term "tangerine" may yet acquire a definite genetic meaning.

In the United States, the “tangerine group” (non-oranges) have taken off in recent years, so people are finally starting to notice them. However, not everybody calls them the same thing. My nieces call the little ones cuties to mirror a brand name. That said, I don’t think they’ve ever tried a kumquat, which gives me a delightful idea for a Christmas stocking stuffer!