As migrating to Lightning from Classic, You will get confused with the way task, event and log a call are different in Lightning.

In Classic, You have Open Activities and Activity History related list available on the page layout. Open Activities lets you create Task and event record with the record type selection functionality (if you are using record type for Task and event in your organization) whereas Activity history will let you Log a call or send an email. Also, both the related list shows the record created by users.

In Lightning, Salesforce has introduced a standard lightning Component which shows the actions to create the task and other action along with an activity timeline which shows the record you have already created. The activity timeline will show the task and events yet to come in the section called Next step while closed one in Past activities section.

The twist is those action inside the standard Activity Component does not come by default. You need to add those action in mobile and Lightning experience section on the page layout.

Note:- Those actions can be a global action or object specific action but if you are having record types for Task and Event Object, You must assign a default record type to those actions.

The problem here is if you are having 4 record type for task object, You need to create 4 actions for each record type of task which can be avoidable, See how:-

Approach-1

Summer 19 comes with a feature where you can configure the activities view on record pages. Steps to follow:-

1. Click on setup and search for Lightning Experience Transition Assistant.
2. select Lightning Experience Transition Assistant
3. You will see this on your screen:-
4. Click on Go to steps under Roll out Phase
5. You will see as below:-
6. Click on Implement Lightning experience features, It will expand the section as below:-
7. Under Configure the activities view on record Pages, You will see two option named as Related List and Activity Timeline.
8. Its time to choose what you want. If you select the Activity timeline, The Activities will continue to come as it was till spring’19. Your action will come under Activity Component on your record Page. When you select the Related list option, It will make activity Component disappear from your record page and will bring two related list called Open activities and Activity History as it was in Classic. The action will derive from the page layout of the record page and depend on what you have configured for those related lists on the page layout.

Note:- When you choose Related List option in Activities Configuration picklist, It will disable the Activities Component under Lightning App Builder.

What if you want a combination of both Activities Component and Related List for Open Activities and Activity History? Check for the second approach where I will not enable Related List under Activities Configuration and will keep Activity Timeline as the preference.

Approach-2

Salesforce has given you a standard component called Related List Single. All you need is to add related list single component to Lightning page layout using Lightning App Builder and select Open Activities in related list names available on the right-hand side panel. Once done, Save the page and activate it for the users you want.

This will let you see the Open Activities Related list with actions to create Task and Event with record type selection functionality. In the same way, You can repeat the process for Activity History related list.