Consider these two categories of illegal positions. First, e.g.:
- Not having exactly one King of each color
- Both Kings being in check
- Pawns on the first or eighth ranks
- Having more than 8 Pawns of the same color
- Having doubled Pawns without the opponent missing any pieces
- Two Knights giving check at the same time
In the first category, the problem with the position is severe enough that it prevents normal gameplay from continuing (e.g., the victory condition is no longer clear, you might try to capture your opponent's King, and the rules don't define how those Pawns could move). In the second category, while an illegal move must have been made to get there in the first place, nothing would go wrong if you tried to continue a game from there. Chess software seems to make this distinction too: https://lichess.org/editor will gray out "Analysis board" and "Study" for the first category but not the second. Is there an accepted terminology to distinguish between these cases, something like "prograde illegal" vs. "retrograde illegal" or "strongly illegal" vs. "weakly illegal"?