Meaning of isostructural
Two species are isostructural if they have the same molecular geometry/shape.

Check each pair

Option A: $CO_3^{2-}$ and $NO_3^-$

• In $CO_3^{2-}$, central atom = C with 3 bonding regions and no lone pair.
• Shape = trigonal planar.
• In $NO_3^-$, central atom = N with 3 bonding regions and no lone pair.
• Shape = trigonal planar.

Therefore, they are isostructural.

Option B: $PCl_4^+$ and $SiCl_4$

• For $PCl_4^+$: phosphorus has 4 bond pairs and no lone pair (positive charge removes one electron from the lone pair possibility).
• Shape = tetrahedral.
• For $SiCl_4$: silicon has 4 bond pairs and no lone pair.
• Shape = tetrahedral.

Therefore, they are isostructural.

Option C: $PF_5$ and $BrF_5$

• $PF_5$: phosphorus has 5 bond pairs and no lone pair.
• Shape = trigonal bipyramidal.
• $BrF_5$: bromine has 5 bond pairs and 1 lone pair.
• Electron pair geometry = octahedral, molecular shape = square pyramidal.

Therefore, they are not isostructural.

Option D: $AlF_6^-$ and $SF_6$

• $[AlF_6]^{3-}$ is the common hexafluoroaluminate ion; central Al has 6 bond pairs.
• Shape = octahedral.
• $SF_6$: sulfur has 6 bond pairs and no lone pair.
• Shape = octahedral.

Therefore, they are isostructural.

Final conclusion The pair in which the two species are not isostructural is: $\boxed{C}$

Comparison with stored correct answer Stored correct answer = $C$.

My derived answer matches the stored answer.