An embedding is a representation of a word that can be used as a proxy for some of its linguistic properties.
The 'human' representation of a word, a sequence of letters and other symbols, is not related at all to its meaning or use in actual text. It only serves as a look-up key into our cognitive language processing facility (however that actually works) which enables us to understand the meaning in the context of its usage. However, a computer system does not have such a facility.
In order to convert the character string into something more usable for language processing, embeddings are created. These are typically vectors describing other words that surround a word in question (as the meaning of a word depends on its context). There are obvious problems with ambiguities (eg is bank the side of a river or a place where you deposit money?), but there are probably ways around that.
So the embedding (a vector) represents the usage of a word, which strongly correlates with its meaning. Because words as character sequences are useless for most sub-symbolic processing, the terms embedding and word are possibly used interchangably.