I am finding a strange inconsistency in sources between those about New Mexico's history and those about Texas. As I know, New Mexico and Texas both started as parts of New Spain, under Spanish rule, but after the Mexican War of Independence, they became part of the United Mexican States.

Under Spain, I find many references of New Mexico being referred to as "the Kingdom of New Mexico", but cannot find similar references to "the Kingdom of Texas". I also see "Province of New Mexico" in some sources. Which is correct?

Similarly, after Mexican independence, these were within Mexico, I find references of New Mexico called "the Territory of New Mexico", but cannot find similar wording in articles to "The Territory of Texas".

What is the correct naming?

1. When referring to these places politically, should I call them kingdoms, or provinces, or territories under New Spain? How about under Mexico?
2. When giving their full official title, but translated for English readers, what is the correct name, "Kingdom of New Mexico", "Province of New Mexico", etc.