Document Properties:
Document properties, also known as metadata, are details about a file that describe or identify it. They include details such as title, author name, subject, and keywords that identify the document's topic or contents.
If you include the document properties for your files, you can easily organize and identify them later. You can also search for documents based on their properties or insert them into your documents.
There are four types of document properties:
Standard properties: By default, Office documents are associated with a set of standard properties, such as author, title, and subject. You can specify your own text values for these properties to make it easier to organize and identify your documents.
Automatically updated properties: These properties include both file system properties (for example, file size or the dates when a file was created or last changed) and statistics that are maintained for you by Office programs (for example, the number of words or characters in a document). You cannot specify or change the automatically updated properties.
You can use the automatically updated properties to identify or find documents.
Custom properties: You can define additional custom properties for your Office documents. You can assign a text, time, or numeric value to custom properties, and you can also assign them the values yes or no. You can choose from a list of suggested names or define your own.
Document library properties: These are properties that are associated with documents in a document library on a website or in a public folder. When you create a new document library, you can define one or more document library properties and set rules on their values. When you add documents to the document library, you are prompted to include the values for any properties that are required, or to update any properties that are incorrect.
Source: View or change the properties for an Office file.
You can see the document properties as shown in below image:

Managed Metadata in SharePoint:
Metadata is data that describes additional information about an item. Or you can say, Metadata is information about information. When you use SharePoint products, you can manage the metadata centrally.
You can read more about managed metadata in SharePoint in below article:
Introduction to managed metadata.