My answer is only a personal opinion and reflects how I understand the IPA terminology. If you take a look at the formal chart of IPA, you can see how and where each vowel is represented:

They are represented in a polygonal shape that depicts the oral cavity. Each vowel is described by terms that indicate its position in the oral cavity such as front, centeral, back on the anterior-posterior axis, and close, mid, open on the superior-inferior axis of the oral cavity. Each vowel is described according to its position in the oral cavity. Vowels are not described according to their relative positions to each others.
E-schwa is defined as:
Its vowel height is mid, which means the tongue is positioned halfway between a close vowel and an open vowel.
Its vowel backness is central, which means the tongue is positioned halfway between a front vowel and a back vowel.
It is unrounded, which means that the lips are not rounded.
This schwa can not be described as *highschwa or *Hochschwa because it does not occur in the upper half of the oral cavity.
A-schwa is defined:
Its vowel height is near-open, also known as near-low, which means the tongue is positioned similarly to an open vowel, but is slightly more constricted – that is, the tongue is positioned similarly to a low vowel, but slightly higher.
Its vowel backness is central, which means the tongue is positioned halfway between a front vowel and a back vowel.
It is rounded, which means that the lips are rounded rather than spread or relaxed.
This schwa occurs in the lower half of the oral cavity, so describing it as a low schwa (Tiefschwa) is legitimate.
In conclusion, there is a schwa, there is a Tiefschwa, but there can not be a *Hochschwa.