First, what is Activity Capture? Its the act of taking communication data such as email, calendar events, and contacts and adding them to your CRM. CRM is your system of record and in the best of all worlds you really want to maintain a healthy CRM so you know about your customers and what is going on with them.
Salesforce has a variety of tools to deal with this including: Salesforce Chrome
Einstein Activity Capture is a great step into bringing salesrep activity data (email and calendar events) into Salesforce. By default Einstein Activity Capture pulls in emails and calendar events and associates them with EXISTING Salesforce Contacts and Accounts.
Note, Einstein Activity Capture does NOT Capture NEW Contacts. Only associates Emails and Calendar Events to Existing Contact/Account Objects.
The Salesforce Chrome Extension is an Addin for Gmail and is available for Free with your Sales Cloud License.
Salesforce Inbox is an additional charge and commonly referred to as Salesforce Inbox Premium.
Both of these solutions from Salesforce are designed as a Productivity Assistant for Salesreps. Which include things like Salesforce Account/Contact lookup, Search, and also the ability to push Events and Emails to Salesforce. Both are