The difference between One-to-many, Many-to-one and Many-to-Many is:

One-to-many vs Many-to-one is a matter of perspective. Unidirectional vs Bidirectional will not affect the mapping but will make difference on how you can access your data.

In Many-to-one the many side will keep reference of the one side. A good example is "A State has Cities". In this case State is the one side and City is the many side. There will be a column state_id in the table cities.
In unidirectional, Person class will have List skills but Skill will not have Person person. In bidirectional, both properties are added and it allows you to access a Person given a skill( i.e. skill.person).

In One-to-Many the one side will be our point of reference. For example, "A User has an Addresses". In this case we might have three columns address_1_id, address_2_id and address_3_id or a look up table with unique constraint on user_id and address_id.
In unidirectional, a User will have Address address. Bidirectional will have an additional List users in the Address class.

In Many-to-Many members of each party can hold reference to arbitrary number of members of the other party. To achieve this a look up table is used. Example for this is the relationship between doctors and patients. A doctor can have many patients and vice versa.