I couldn’t have described it better myself. I’d say that the neo-pagans would also include witchcraft-based groups, which, admittedly, do sometimes incorporate nature worship. I’d consider Wicca pagan even though I don’t think they always include nature/earth worship or worship of ancient deities, unless “Goddess worship” counts as the latter.
I, as a Pagan and a Wiccan, do identify with what you’ve said here. More information abut the term follows here from an on-line dictionary:
Etymology: Middle English
pagan “heathen,” from Latin **paganus **(same meaning), from earlier
paganus “person who lives in a rural area,” from *pagus *“village, district”
Word History: In ancient Rome a person living in a rural area or village was called paganus, a word derived from the Latin noun pagus, meaning “village, district.” In time paganus came to refer to a civilian as opposed to a soldier. When Christianity became generally accepted in the towns and cities of the empire, paganus was used to refer to a villager who continued to worship the old gods. Christians used the term for anyone not of their faith or of the Jewish faith. The word in Old English for such a person was what is now heathen. In the 14th century, English borrowed the Latin paganus as pagan, and used it with the same meaning. In time both heathen and pagan also took on the meaning of “a person having no religion.”
However, James J. O’Donnell of the The Catholic University of America in Washington DC delves deeper still. Here is a link to a very detailed article regarding his analysis surrounding the term:
www9.georgetown.edu/faculty/jod/paganus.html
Wikipedia states that:
EXCERPT (link below): “. . . Paganism is a broad group of indigenous and historical polytheistic religious traditions—primarily those of cultures known to the classical world. In a wider sense, it has also been understood to include any non-Abrahamic folk/ethnic religion.
The term pagan was historically used as one of several pejorative Christian counterparts to “gentile” (גוי / נכרי) as used in the Hebrew Bible—comparable to “infidel” or “heretic”. Modern ethnologists often avoid this broad usage in favour of more specific and less potentially offensive terms such as polytheism, shamanism, pantheism, or animism when referring to traditional or historical faiths. Since the 20th century, “Paganism” (or “Neopaganism”) has become the identifier for a collection of new religious movements attempting to continue, revive, or reconstruct historical pre-Abrahamic religion. There are roughly 300 million pagans worldwide.” (footnotes omitted herein)(
bolded portion very similar to Mr. O’Donnell’s analysis, of which I did not quote an excerpt as to do so would be too limiting)
And lest we forget, ". . . Christianity itself has been perceived at times as a form of polytheism by followers of the other Abrahamic religions because of the Christian doctrine of the Trinity (which at first glance might suggest Tritheism,) or the celebration of Pagan feast days and other practices – through a process described as “baptizing” or “Christianization”. Even between Christians there have been similar charges of idolatry levelled, especially by Protestants, towards the Roman Catholic and Orthodox Churches for their veneration of the saints and images. . . " (footnotes omitted herein)
Wiki also includes a section entitled Contemporary Paganism which is quite good and very detailed.
en.wikipedia.org/wiki/Paganism
So,
what is a Pagan?

It entirely depends upon whom you ask… and what the asker actually seeks.
Namaste.