Memberships will capture the start date/end date of entire Membership(s) with an Organisation, whereas Subscriptions will look at the start and end date of just their current Membership.

A contact that has an 'Active' Membership.
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When a contact has no active memberships, they're typically referred to as a contact – although, since everyone is a contact, this term is interchangeable.
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An instance of an Active Membership Level. 

It's possible to have many memberships for a single contact and many contact's for a single membership.
For example, you can have a family membership with many members. Consider a basic family membership with Two Adults and Two Children. This would count as one membership, and four members.

Holds all the information about a membership; description, date rules and prices. 

Memberships are based on membership levels and members are assigned to memberships. 

A Membership is made up of multiple Subscription periods... so each time a Contact renews, they are obtaining another Subscription.

e.g. a Contact could have a Membership of an Organisation that spans years (e.g. 2018-2021) but their Subscription would be for the individual Membership periods (e.g. 2018, 2019, 2020 etc).