This supposedly simple question disguises one of the most important problems for students of English. This problem is called understanding the meaning of the verb phrase. Since understanding the meaning of the verb phrase is ubiquitous all along any stage of learning English, you should decide how to solve it in some correct way as soon as possible. You must confidently use an accepted approach in further learning.
The verb phrase is of the six types of so-called verb patterns. One of these verb patterns is a pattern of the form SV (Subject + Verb). That is, the intransitive verb is used in this pattern. This pattern is used in the example and, respectively, both the verbs work and work out are intransitive. An intransitive verb is one that does not have to be followed by an object.
Within each basic pattern form mentioned above, we can distinguish a varying number of subpatterns. It is not possible to list every verb which can occur in each pattern or subpattern. For this you will need to consult a dictionary.
In order to master the typical use of verbs in English and their meaning in sentence, the so-called learners' dictionaries are suitable, for example, Collins COBUILD Advanced Learner's Dictionary.
Presence of a particle changes the meaning of a verb. In accordance with it, the verbs work and work out are the verbs having different meanings. The verb work out is called a phrasal verb, or an idiom. An idiom is a string of fixed words having a meaning that is not deducible from the meanings of the individual words that are formed to be a phrasal verb.
Then, you should evaluate a probable meaning of the sentence (utterence) in question in order to choose a meaning of the verb from the dictionary, which is most suitable for the meaning of the sentence that has been evaluated.
This way we can choose the meaning of 'if a system of doing something works, it is effective, successful or satisfactory' for the first example; and, 'if a situation works out, it happens or progresses in a satisfactory way' – for the second one.