It depends. There are a few different ways these words relate to each other:
1) The form with "-al" is an adjective, and the form without is a noun. That's the case with "logical" vs. "logic". The former is always an adjective, and the latter is always a noun. Other examples are "musical/music" and "ethical/ethic".
2) The form with "-al" is an adjective, and the form without is an adjective or a noun. The adjective form without "-al" might mean the same thing as the form with "-al". An example of that situation is "magical/magic". But the meanings could differ, as in "graphical/graphic". "Graphic" as an adjective is sometimes a synonym of "graphical", meaning "having to do with images", and sometimes has a very different meaning — "highly descriptive, especially of sex or violence".
A special case is "arithmetical/arithmetic", where "arithmetic" is stressed on the second syllable when it's a noun and on the third syllable when it's an adjective.
3) Both words are adjectives, as well as synonyms. Examples include "geographical/geographic" and "biographical/biographic".
4) Both words are adjectives, but they have different meanings. One example is "economical/economic". "Economic" means "having to do with the economy", but "economical" means "saving money, thrifty". Another instance is "historical/historic"; "historic" means "famous or important in history", while "historical" just means "having to do with history".
As you might notice, there isn't a neat pattern to these word pairs. Some are synonyms, and some aren't. Some are different parts of speech. The correct usage has to be learned on a case-by-case basis.
N'hésite pas à corriger mes erreurs.