Botocore is the foundation that underpins the AWS CLI and also Boto 3, while Boto 3 is the official python SDK for AWS.

As others have said, Boto3 provides a cleaner API which will make your code more readable. Consider the following example usage, both examples achieve the same result but Boto 3 does it with fewer lines and fewer characters:

Botocore:

import botocore.session
session = botocore.session.get_session()
client = session.create_client('ec2', region_name='us-west-2')
response = client.describe_instances()

Boto 3:

import boto3
ec2 = boto3.client('ec2')
response = ec2.describe_instances()