The math
Bi-weekly is every other Friday: 26 paychecks per year. Semi-monthly is twice a month, typically the 15th and last day: 24 paychecks per year. Same annual salary divided by different numbers gives different per-paycheck amounts. Bi-weekly checks are smaller per period than semi-monthly because the salary is divided by 26 instead of 24.
The "extra" paycheck illusion
Bi-weekly schedules produce 26 paychecks per year, but two months a year contain three paychecks instead of two. People treat those as bonuses. They are not bonuses, just the natural result of the calendar.
Tax withholding
Annual tax owed is the same regardless of pay frequency. Per-paycheck withholding is calculated to total to the same annual tax. The IRS Publication 15-T tables include both bi-weekly and semi-monthly variants.
Benefits and 401(k) timing
Some plans use bi-weekly contributions, others semi-monthly. Annual contribution limits are the same. Employer match formulas may use a per-paycheck cap that interacts differently with each schedule, check your plan documents.
What is better?
Personal preference. Bi-weekly aligns with a weekly budget rhythm. Semi-monthly aligns with monthly bills. Both end up at the same annual total.