different between notional vs theorical

English

notion +? -al

notional (comparative more notional, superlative most notional)

Of, containing, or being a notion; mental or imaginary.
Speculative, theoretical, not the result of research.
This paper proposes a notional Federated Identity Management (FIM) architecture.
(linguistics) Having descriptive value as opposed to a syntactic category.
(finance) Used to indicate an estimate or a reference amount
(informal) Full of ideas or imaginings.
- 1995, Walter D. Edmonds, In the Hands of the Senecas (page 137)
  She knew what Pete would say if she told him about it — he would say she was getting notional; and she did not want Pete to think of her as a notional woman. Notional women sometimes had a hard time marrying unless they had money.

notional (plural notionals)

A fake company used as a front in espionage.
- 2012, Joseph C. Goulden, Peter Earnest, The Dictionary of Espionage: Spyspeak Into English (page 157)
  Numerous CIA notionals, created to counter Communist organizations in Western Europe during the Cold War years, remain active and unrevealed.

theorical (not comparable)

Send