REST API

REST API is mainly used for  ease of integration and development. It
supports smaller sets of data.

SOAP API

SOAP API cab be written in any language that supports Web services.
For example, you can use SOAP API to integrate Salesforce with your
organization’s ERP and finance systems, deliver real-time sales and support
information to company portals, and populate critical business systems with
customer information.

Chatter REST API

Chatter REST API provides programmatic access to Chatter feeds and social data
such as users, groups, followers, and files.

Bulk API

Bulk API is based on REST principles and is optimized for loading or deleting
large sets of data.
Bulk API is designed to process data from a few thousand to millions of
records.
The easiest way to use Bulk API is to enable it for processing records in Data
Loader using CSV files. This avoids the need to write your own client
application.

Use Metadata API

Use Metadata API to retrieve, deploy, create, update, or delete customizations
for your organization. The most common use is to migrate changes from a sandbox
or testing organization to your production environment. Metadata API is
intended for managing customizations and for building tools that can manage the
metadata model, not the data itself.
The easiest way to access the functionality in Metadata API is to use the
Force.com IDE or Force.com Migration Tool.

Streaming API

Use Streaming API to receive notifications for changes to data that match a
SOQL query that you define.
Streaming API is useful when you want notifications to be pushed from the
server to the client. Consider Streaming API for applications that poll
frequently. Applications that have constant polling action against the
Salesforce infrastructure, consuming unnecessary API call and processing time,
would benefit from this API which reduces the number of requests that return no
data.Streaming API is also ideal for applications that require general
notification of data changes. This enables you to reduce the number of API
calls and improve performance.

Apex REST API

Use Apex REST API when you want to expose your Apex classes and methods so that
external applications can access your code through REST architecture. Apex REST
API supports both OAuth 2.0 and Session ID for authorization.

Apex SOAP API

Use Apex SOAP API when you want to expose your Apex methods as SOAP Web service
APIs so that external applications can access your code through SOAP. Apex SOAP
API supports both OAuth 2.0 and Session ID for authorization.

Tooling API

Use Tooling API when you want to manage and deploy working copies of Apex
classes and triggers and Visualforce pages and components, set checkpoints or
heap dump markers, execute anonymous Apex, and access logging and code coverage
information.