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If social security and Medicare taxable wages are calculated the same, why are the amounts in boxes 3 and 5 on my W-2 different?

The amount in W-2 box 3 represents "Social Security Wages." The amount in box 5 is "Medicare Wages." There is no maximum amount for Medicare Wages. However, there is a calendar year maximum for an employee's "Social Security Wages." Once that maximum is reached, social security taxes no longer apply for that calendar year. The yearly maximum for social security typically changes each year: 

2020 - $137,700

2021 - $142,800

2022 - $147,000

2023 - $160,200

2024 - $168,600

In addition, some employees are exempt from social security but not Medicare, and that would therefore result in social security and Medicare amounts not being equal.