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When processing the simple file:

documentclassreport

begindocument
1234567890

$1234567890$
enddocument

with pdflatex one get a PDF with one font only (CMR10), but when processing with either xelatex or lualatex the produced PDF use Latin Modern Roman 10 outside math-mode and CMR10 inside.

What are the reasons behind this?

Since TeX Live 2018 LaTeX now UTF-8 by default, because the “Unicode revolution” has been completed¹. This makes it superfluous to add usepackage[utf8]inputenc when using pdfLaTeX.

The UTF-8 support in pdfLaTeX is fake however and you cannot expect to get a meaningful output when you paste arbitrary UTF-8 characters into the input, because the underlying pdfTeX engine is inherently limited to 8-bit encoding.

This is quite different with Xe/LuaTeX. These engines support UTF-8 by default². Traditional TeX fonts are very limited in the glyphs they offer³. This is definitely not enough to describe UTF-8, so the font also has to cover the full UTF-8 range⁴. To this end the TU encoding was introduced.

By default LaTeX loads the Computer Modern (CM) family of fonts. The CMR10 font is not available in TU encoding (and never will be), therefore its closest relative Latin Modern Roman 10 is loaded instead.

Now the question remains, why is Latin Modern not used in math mode? That is because in math mode things are a little more tricky. The traditional setup was to have different families and commands like mathbf, mathcal, etc. switched to a different family. This is no longer possible in Unicode, because all the symbols come from a single font. Therefore the family switching approach doesn't work anymore and has to be replaced by a much more complex system which swaps mathcodes back and forth. This is implemented in the unicode-math package. You'll also notice why this is problematic because with the unicode-math package TeX is suddenly much slower due to having to reassign thousands of mathcodes all the time. That is why currently standard OML/OMS encoding is retained.

¹ Everyone stores their files in UTF-8 nowadays and most software understands UTF-8. Just think of Emojies (they are everywhere). They are part of UTF-8, so everything that can display Emojies has to support UTF-8.
² in fact LuaTeX will reject your file if it is not UTF-8
³ T1 encoding can only encode 256 glyphs
⁴ whether the font has the required glyph is another question

The font setup for text and math are quite separated tasks in TeX -- text fonts has to care about things like accented chars and hyphenation, math fonts about lots of symbols and correct placement of sup- and superscripts.

Your example uses only a few glyph which in pdftex can be taken from the same font. But if you add e.g. a minus (-), or chars (abc) the used fonts will be different inside and outside math. And if you switch to the recommended T1-encoding for the text with usepackage[T1]fontenc there will be even differences for the numbers.

For the unicode engines there is a difference even in the default setup as the use of a unicode font as text font is more or less mandatory to get accented chars and hyphenation right (see e.g. https://tex.stackexchange.com/a/470987/2388). So at the begin of 2017 the LaTeX-kernel changed the default for this engines so that users weren't forced to load fontspec anymore.

In math hyphenation and accented chars are not really relevant, so the legacy math setup works find in the unicode engine. But even if the math setup is changed to use an unicode font it wouldn't be the same as the textfont but e.g. latin modern math.