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Some people may be qualified for both programs. You can't receive benefits from both at the same time. But you can receive from one program and then from another. 

Eligibility:

CERB - workers who earned in 2019 or in the last 12 months, at least $5,000 in employment or self employed income AND who earned no income for at least 14 consecutive days.
EI - employees who contributed to EI or self employed who registered for EI and worked 12 months. Accumulated between 600-700 ensurable hours. Eligible if got laid off, sick, quarantined, or taking care of a family member.

When is available:

CERB - March 15 - Oct 3, 2020
EI - Any time if eligible

How much:

CERB - $2,000/month
EI - 55% of usual pay to a maximum of $573 per week.

Length of payouts:

CERB - 16 weeks
EI - 15 weeks

How to apply:

CERB - My account on CRA website. Need to setup an account. https://www.canada.ca/en/revenue-agency/services/e-services/e-services-individuals/account-individuals.html
EI - My service Canada account and need ROE from employer. Need to setup an account if never received EI or maternity. https://www.canada.ca/en/employment-social-development/services/my-account.html

First payment ETA:

CERB - Government promised 10 days after the application if choose a cheque or 3 days if direct deposit.
EI - on Service Canada website, the government is stating that there is a large backlog and hence it may be a longer wait to get approved for EI.