@โจ *****
No. A contract is what they give you when you're first employed and outlines all the conditions of employment such as: work hours (for example, 9am-5pm), lunch break (for example, 45 mins), sick leave entitlements, personal and vacation (holiday leave) entitlements, company dress code (not really relevant for a remote position but you get my drift). Salary is usually mentioned and a contract can, in some cases, be tens of pages long.
An employment certificate is usually just one page long and verifies that you are employed by X company (can include a short statement of what the company does), your duties, how long you've been employed, salary can be stated but doesn't need to be, and is often addressed to the consulate you're applying to, since this letter is written for the purposes of applying for a visa application. Employer certificates used for other purposes would be written in a similar way but addressed to the relevant parties.