Plain version: some health and disability terms work like a deductible, but they are measured in days instead of dollars. Keep three apart by asking when each one starts and what it holds back.
Elimination period: the time after a disability begins during which no benefit is payable, a deductible measured in time. It runs from the start of each disability. Example: a 90-day elimination period and $3,000 a month, with no retroactive payment. Counting 30-day months, a 210-day disability is paid for the last 120 days, or 4 months at $3,000 = $12,000.
Probationary period: a stated number of days right after the policy begins during which sickness is not covered. It runs once, from the policy's start, and usually does not apply to accidents. It guards against people who buy coverage when they already feel ill. (In group plans the phrase is sometimes used for a new hire's wait for eligibility.)
Waiting period (group health): the time that must pass before coverage for an otherwise eligible person can take effect. Federal rules bar any waiting period over 90 days in group health coverage. California adds that a health benefit plan itself shall not impose a waiting period (Ins. Code §10198.7(c)), so in practice any wait comes from the employer's own eligibility rule.
Waiver of premium: keeps the policy in force without premium payments while the insured is totally disabled, usually after the disability has lasted a stated period. Premiums are waived for as long as the total disability continues. When the insured recovers, premium payments simply start again. Waived premiums are forgiven, not a loan, so nothing is repaid.