Optimal is an adjective only: "the optimal route". Optimum is both a noun and an adjective — you can reach an optimum, or take the optimum route. Where both fit, either is correct. What neither means is "very good": an optimum is the single best point under the given conditions, so "more optimal" is a contradiction.
The core difference
The grammatical split is small and easily stated. The meaning problem underneath it is the one worth attention.
Grammar
- optimal — adjective only: the optimal temperature
- optimum — noun: the optimum lies near 40°C; adjective: the optimum temperature
Where an adjective is needed, both work and the choice is stylistic. Optimal is more common in technical writing; optimum feels slightly older.
The meaning worth guarding
An optimum is the best under given constraints — a single point, not a general compliment. That is why more optimal, most optimal and very optimal jar: they treat a superlative as though it had degrees. If you mean "better", write better.
Plural
The noun takes optima or optimums. Both are accepted; optima is usual in scientific writing.
