I think you may have a few things confused here Alice. Dealing with the disability system that's rather easy to do. I had a talk with a legally trained expert in disability and learned the following:
You might take a look at the very comprehensive thread at http://forums.webmd.com/3/chronic-disease-and-disability-exchange/forum/984 of webMD (you will have to establish an acct, but it's free and doesn't obligate you to anything). Also pertinent is http://www.ssa.gov/redbook/eng/overview-disability.htm#a0=3, containing a very helpful chart comparing the two programs (soc sec disability ins, SSDI, and supplemental security income, SSI).
(1) Both SSDI and SSI are federal programs; however, initial disability determinations are usually delegated to the states; this doesn't make the programs into state programs, it just delegates the task of the initial determination to a state agency.
(2) SSDI and SSI are two separate programs; that is, the benefits from one come from a separate, different fed govt fund than the benefits from the other. However, a person has to be "disabled" (as defined by fed law) to qualify for benefits from either program. SSDI and SSI come from separate fed govt funds because they have different purposes -- SSDI is to replace part of the income of a person who worked for a certain amt of time and earned a certain amt of money over their lifetime (both defined by fed law) but is now disabled; SSI is to ensure that a disabled person has a certain amt of money to live on (a fixed amt defined by fed law), whether or not they worked and no matter how high/low their lifetime earnings were.
(3) Because the programs have different purposes, the benefits under each are calculated differently. SSDI benefits are calculated based on past earnings, whereas -- loosely stated -- SSI benefits are calculated based on an amt considered to by congress to be a necessary minimum income.
(4) It is possible to be be eligible for benefits from both programs at once. for example, as noted above, a disabled person will be entitled to benefits under SSDI if that person worked for a certain amt of time and earned a certain amt of money over his/her lifetime. However, because SSDI benefits are correlated to lifetime earnings, if your lifetime earnings were relatively low, then SSDI benefits will also be relatively low. Under SSI, in contrast, Congress establishes a certain fixed amt as a necessary minimum income for a disabled person; therefore, even for a disabled person entitled to benefits under SSDI, if the SSDI benefits are not as high as the person's benefits would be if calculated under SSI, s/he will also be entitled to a supplement from the SSI fund to bring his/her total benefits up to the necessary minimum income that congress has set.
(a) based on a disabled person's lifetime earnings, his/her SSDI benefits are calculated to be $400/month ($4,800/year).
(b) however, congress has set the necessary minimum income for a disabled person for that year (SSI program) to be $1,000/month ($12,000/year).
(c) the SSDI benefits are only $400/month ($4,800/year), therefore the person is entitled to SSI benefits of $600/month ($7,200/year) as well, in order to bring the person's total benefits to the amt congress has determined is the necessary minimum income for a disabled person ($400 SSDI + $600 SSI = $1,000/month; $4,800 SSDI + $7,200 SSI = $12,000/year).
(a) based on a disabled person's lifetime earnings, his/her SSDI benefits are calculated to be $2,000/month ($24,000/year).
(b) congress has set the necessary minimum income for a disabled person for that year (SSI program) to be $1,000/month ($12,000/year).
(c) since the SSDI benefits exceed the necessary minimum income amt set for the SSI program, the person is not entitled to any supplement from that program.
(5) Some states have set their own necessary minimum income at an amt higher than the fed SSI program does. In those cases, each state makes an additional grant of benefits in order to increase a disabled person's benefits to that state's own determination of a necessary minimum income. For example, a state sets its own necessary minimum income for a disabled person at $13,000/year. In addition to the $12,000 in fed benefits (both SSDI and SSI) the person would receive, therefore, the state would grant the person another $1,000/year, in order to bring the person's total income to $13,000.
(6) With respect to health care programs, medicaid is for people of low income (altho primarily funded by the fedl govt, coverage and income requirements are determined by each indiv state). Eligibility is based solely on income, and a person does not have to be disabled to be eligible. I'm uncertain if there is a waiting period after it is determined that a person qualifies (i doubt it, but i don't know for sure).
(7) Medicare is for people over 65 and disabled people of any age. Once a person is approved for disability payments, they receive medicare coverage after two years or whenever they turn 65, whichever is sooner.
(8) The five-month waiting period that your correspondent refers to is the interval between what is determined to be the date of onset of a person's disability (or date of application, depending on whether you are eligible for SSDI or only SSI) and the date when you actually begin receiving the benefits.
I hope this is useful as a starting point.