A rising aerial is a term for doing an aerial straight out of a jump.
For example, I can jump, and instantly use Fair - this is a rising Fair.
It doesn't matter whether they are done in a short hop or a full hop; you're still rising in both, but they can be used in different situations.
For example, short hop rising Fair with Marth is generally less safe than full hop rising Fair, but both have different uses. Short hop rising Fair is good while retreating (jump and use Fair, and move backwards while doing so), but full hop rising Fair is good when combined with a fast falling Nair.
So yes, falling aerials exist too, and they're exactly what they sound like. However, there are falling and fast falling aerials, and if you know what a fast fall is, you will know what a fast fall aerial is.
Of note, if you fast fall first, then aerial, your fast fall momentum will cancel. You can remedy this by holding down on the control stick and using your C-Stick to aerial, as you will essentially fast fall again instantly as you use your aerial. This makes certain spacing moves easier to use, such as Rosalina, Bayonetta and ZSS Back Aerials.
