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Matzah on Pesach can be made from white (refined) or whole grain wheat (or any of the other allowed grains).
Did our ancestors typically bake with refined or whole grain wheat?
Were the first matzah white (refined) or whole grain wheat?
Why do we see more white (refined) matzah nowadays?
The flour used to bake matzot has changed through the years. However, grains have soaked to enable separation of the bran and germ (present in whole wheat) from the starchy endosperm (what makes the "white" in white flour) for almost all recorded history (will get you a citation later).
The Egyptians generally had pretty bad flour, using soft stones to do their milling. They often wound up with lots of rock dust mixed in with their flour. See "On Food and Cooking" for more details. So, presumably the first matzot were made with flour like this, likely from Khorasan-ancestor wheat.
Zohar Amar claims that matzah used to be baked with a coarse-ground flour, much like semolina, but I don't think his claims are convincing. See his book חמשת מיני דגן.
There is a disagreement among the Amora'im regarding this question:
אמר רבה בעל נפש לא ילתות מאי איריא בעל נפש אפילו כולי עלמא נמי דהא תניא אין לותתין שעורין בפסח הכי קאמר בעל נפש אפי' חיטין דשרירי לא ילתות א"ל ר"נ מאן דציית ליה לאבא אכיל נהמא דעיפושא דהא בי רב הונא לתתי ובי רבא בר אבין לתתי ורבא אמר אסור ללתות
Rava initially felt this was not a good idea (he eventually changed his mind), and Rav Nachman basically said whoever holds like Rava is eating terrible bread (the "white vs whole wheat" debate is fairly old!). Since Rava changed his mind and said that it's obligatory to soak the grains (and thus have white flour) -- "הדר אמר רבא מצוה ללתות" -- it seems that in the times of the Talmud, most people baked matzah preferentially with white flour.
However, from the times of the Ge'onim and on we no longer soak grains. See, for example, Rambam (easier to find the source online, but it's explicit in the Geonim):
וּכְבָר נָהֲגוּ כָּל יִשְׂרָאֵל בְּשִׁנְעָר וּבְאֶרֶץ הַצְּבִי וּבִסְפָרַד וּבְעָרֵי הַמַּעֲרָב שֶׁלֹּא יִבְלְלוּ הַחִטִּים בְּמַיִם גְּזֵרָה שֶׁמָּא יִשְׁהוּ וְיַחֲמִיצוּ:
Thus, in the middle ages most flour was likely coarsely-sifted whole wheat. Nowadays, most "white" matzah flour today is actually partially whole wheat (about 60% extraction), since it's stone ground whole wheat that's sifted.
