會 is a modal verb.
From the classic Li & Thompson (1981) Mandarin Chinese: A Functional Reference Grammar:
Most languages have morphemes for signaling the of a reported event relative to the time of speaking (tense) or the duration or completion of a reported event relative to other events (aspect)...
會 and 要 are on the other hand examples of the last portion of the T-A-M trinity for verb morphology: M for mood or modality. The standard moods in Western European verb morphology are: indicative, subjunctive, conditional and imperative. Other examples are optative, jussive, hortative, interrogative and volitional.
In Mandarin Chinese, 會 can act as an epistemic modal, i.e. with the idea of ways of knowing and confidence in the knowledge. These are of the same category as 可能 and 應該. As well as being like a "potential" mode, it is can act as a "conditional":
Tā rúguǒ qù kàn yákē jiù huì chí dào.
If she has gone to see the dentist, then she'll be late.
These words are definitely in a different category to the aspect particles 了、過、著, because 會 can be combined with them, under certain circumstances:
Tā bù huì qù-le Zhōngguó!
He can't have gone to China!
On the other hand, 要 is a deontic modal, expressing shades of obligation / permission, and is in the same category as 可以 and 得 (děi).
These are actually very similar to English will, which derived from the modal verb meaning "want" (compare its noun form e.g.
the will of the people, which retains that older meaning), and English shall deriving from a modal verb meaning "should" or "ought to" (compare its German cognate
sollen). The future tense meaning is naturally implied.
Also, there are restrictions for both languages on which modal can combine with which aspect marker. Only a select set of verbs can take both "future"-orientated modal markers and perfective 了 at the same time, e.g. 饒 ráo:
Nǐ yào ráo-le tā ma?
Are you going to spare/forgive him?
Nonetheless, perfective 了 and experiential 過 aspect markers can appear with the future-orientated modal 會 or others when occurring in a non-final event clause in a sequence:
Wǒ huì cí-le xíng zài dòngshēn.
I will say goodbye / take leave then get up and go.