C23 = uncoated C2-C3
C23J = uncoated C2-C3 POLISHED
C56 = uncoated C5-C6
323 = main grade C2-C3-C5-C6 coated. Also in 323F (TiALN) and 323FG (TiALN + TiN)
356 = C5-C6 steel grade coated. Also in 356FG (Tialn + TiN)
On all NOTCH style inserts, the first letter begins with "H" for HORIZON. To cross-over... if you used FLG or NG that same insert from us would be the HG series. If you used FLT or NT that same insert from us would be the HT series. Very simple.