𓊹𓌃 madu noutjer
Hieratic

is a Greek word /ἱερατικά γράμματα / hieratika yrammata meaning 'priestly writing' and was a cursive writing system of Hieroglyphics. The Egyptians did not make a distinction between carved hieroglyphics and written they both were called /mdw nTr/. Becuase it was easier then carving Hieratic was used for documentation in Egypt as well as Nubia. It was the most wide spread and most used version. It was also mostly written with reed pens, ink and on papyrus or other such materials, but was occasionally used almost like cuneiform. This version of mdw nTr allowed scribes to be quicker and more efficient in writing. It was originally developed only for religious texts and was considered more of an important writing system then Hieroglyphics being the script used in daily life and documentation. The system of writing was first taught to student scribes, while only very few talented scribes went on to learn Hieroglyphics. Hieratic differs from Hieroglyphics in that it is only written from right to left and in columns or horizontal lines unlike Hieroglyphics which can be written in any way.

The Edwin Smith Surgical papyrus in Hieratic and Hieroglyphics 
http://oi.uchicago.edu/sites/oi.uchicago.edu/files/uploads/shared/docs/oip4.pdf

𓏞𓈖𓈙𓂝𓏏𓍼 𓏥 sekha en shāt
Demotic

is a Greek word /δημοτικός γράμματα / dēmotikós yrammata meaning 'popular writtting' was derived from northern forms of Hieratic. The Egyptians called it sesh en shat meaning 'inscriptions of letters'. It is based off of late Egyptian and predates Coptic. Eventually Demotic cursive replaced Hieratic as the main script in Upper Egypt and was strictly used as administrative, legal, and commercial texts while Hieratic and Hieroglyphics were used for everything else. The Greek language starting to replace Demotic and it helped with the development of Coptic.



******As a note sometimes the Hieratic or Demotic space will have more then one glyph. That means there is more then one example of the letter in the cursive script. All Demotic and Hieratic drawn by me. *******

More on Demotic 
https://oi.uchicago.edu

Pre-Late Kingdom pronunciation guide 1
Pre-Late Kingdom pronocication guide 2


Demotic dictionary 
​https://oi.uchicago.edu/research/pubs/catalog/cdd

Uniliterals

A

Coptic Ⲁ/a

a

b

Coptic Ⲃ/b or Ⲡ/p

d

Coptic Ⲇ/d

D

Coptic Ϫ/ dj

f

Coptic Ϥ/f

g

Coptic ⳉ/kha, gh ?

h

Coptic Ϩ/ h

H

Coptic Ϩ/ ḥ, h

i

Coptic ⲓ/i , ⲈⲒ/ ï

k

Coptic Ⲕ/k ,Ϭ/ch

m

Coptic ⲙ/m

n

Coptic Ⲛ/n

​l (Late kingdom), rw (middle-)

Coptic Ⲣ/r, Ⲗ/l

p

Coptic Ⲡ/p , Ⲃ/b

q

Coptic Ⲕ/k , Ϭ/ ch

r

Coptic Ⲣ/r, Ⲗ/l

s

​Coptic Ⲥ/s

s, z

Coptic Ⲥ/s

S

Coptic Ϣ/sh

t

Coptic Ⲧ/t 
IPA : ​/t̪/

T

w

Coptic ⲞⲨ/ou

w

x

Coptic Ϩ/ h, ḥ, Ϣ/sh

X

Coptic Ϩ/ h, ḥ

y

wA/ō

Coptic Ⲱ/ō

ref
http://ccdl.libraries.claremont.edu/cdm/ref/collection/cce/id/2027​ , Ebers papyrus , A very Brief Introduction to Hieratic by Joshua Aaron Roberson, Demotci Egyptain Guide Texts, exersises and vocabulary , Aoractical grammer for self-study by Leonardo Caldas Vieira