You touched upon the difference between two complimentary themes - emunah vs. bitachon. Ramba"m discusses this quite extensively. I'll try to link a source, later, b"n.
However, I think that this article explains the main concepts quite well. The example about Pharoah to illustrate the difference, I think, is very good. Some excerpts:
The Rambam defines emunah as the knowledge that HASHEM created and
continues to run all of Creation. Simply put, nothing can exist and no
activity can occur without HASHEM.
Bitachon, however, is a quite different. The Chovos Halevovos defines
bitachon as trusting in HASHEM. It is a sense of relying on HASHEM to
watch over and protect me, as if to say, “I take my heavy burden and
place it on HASHEM.” While I am responsible to be proactive, I am not
in charge of the outcome, and I am not the determinant of the results.
I rely on HASHEM to care for me.
Emunah is a state of understanding; bitachon is a state of trust.
Emunah means knowing that HASHEM is involved in every activity on the
planet; bitachon means trusting in HASHEM in every situation.
A person can have emunah and not bitachon
Aperson can have emunah and not bitachon. Pharaoh was a classic
example. When threatened by the Jewish overpopulation, Pharaoh’s
solution was to throw the baby boys into the Nile. The Medrash
explains that this wasn’t a flippant reaction – it was highly
calculated. Pharaoh knew that HASHEM promised Noach that He wouldn’t
bring another flood. He also knew that HASHEM pays back “measure for
measure.” Therefore, Pharaoh determined that HASHEM would want to
bring a flood to pay back the Egyptians for drowning the babies, but
because of HASHEM’s promise to Noach, that couldn’t happen, so he felt
protected from HASHEM’s wrath.
Clearly, Pharaoh understood the power of HASHEM. He realized that
HASHEM watches over the world. He also understood that HASHEM acts
with justice. Pharaoh had no problem with emunah, but he sure didn’t
trust in HASHEM – he rebelled. He had emunah, but no bitachon.
Growing in emunah
Both emunah and bitachon are based on relating to the world in a
deeper manner. Emunah is the understanding that HASHEM is involved in
more than just the big picture issues: life and death, war, famine,
disease. . . HASHEM is involved in the minutiae of my daily life.
HASHEM is there with me, 24/7, 365, all day, every day, from morning
Amazingly, I can have this understanding and yet lack a level of trust
What I infer from this is that emunah is not "blind" faith. If it were, we'd be "dummies" or "zombies", just performing our activities without thinking through it at all. It seems that emunah requires at least some minimal understanding that G-d exists and is in control of all. Atheists, thus, have no emunah, based on this definition. Perhaps, this is why David in Tehilim (I think it's ch. 11 or 13?) calls them fools.