No need to apologize, I am here to help as best I can.
Agender does tend to refer to someone who does not have a gender identity (variously interpreted as genderless, or genderfree). Check out this post for defining genderless, agender, and neutrois:
Agender people may or may not identify as genderqueer. While genderqueer does typically refer to genders that are queer (i.e. non-normative), not every one may be comfortable with what the term queer entails. Other than being an increasingly common umbrella term for non-normative identities and non-normative expressions, “queer” has strong ties to what is radical, political, and Western - not everyone is going to feel this applies to them, even if they have a gender that could be considered queer. Additionally, genderqueer continues to be used in a broad umbrella sense, sometimes including people who’s gender expression is queer, even if they are binary-identified - this raises issues of appropriation and can cause people unfamiliar with genderqueer identity possibilities to make assumptions about people who identify as GQ. These reasons are why the term non-binary has gained increased currency, as it refers to genders that are not binary, without the additional baggage that queer can sometimes hold.
Asexual people may feel similarly about the matter in that some are not comfortable with the term queer in application to their identity, although others are. Queer is a convenient umbrella term more generally and inclusion under the umbrella is often seen as a move of acceptance, but as for individual cases, it is up to how someone is comfortable identifying and queer is not always appropriate, so it is best to clarify if unsure. You may also want to check out this post I made on the difference and relationship between the terms non-binary and genderqueer:
I hope this helps!