I think you're mixing up SSP and ESA, OP.
SSP is for people who are off sick from their job. It's £92.05/week, payable for up to 28 weeks. To qualify you need to have been off sick for 4 or more days and usually earn at least £116/week. It's not means tested. You may also be entitled to means tested benefits depending on household income and savings, e.g. housing benefit and child tax credit, or UC. Also council tax reduction.
After 28 weeks, if you are still not well, or if you don't qualify for SSP in the first place, you can claim ESA. There are two types - contributory and income based.
You can get contributory ESA if you have paid enough NI over the past 2 years. It's not means tested so you can get it even if you have a partner on a good wage, or lots of savings. Usually this lasts for up to a year, but it can last indefinitely if you are so unwell you are assessed as having limited capability for work and work related activity, and placed in the 'support group'.
After your contributory ESA runs out, or if you didn't qualify for it in the first place, you can claim income based ESA. As the name suggests this is means tested.
When you first claim ESA you get £73.10/week (or £57.90 if you are under 25) This lasts for the 13 weeks while you are assessed for capability for work. After this -
If you are assessed as having limited capability for work you get £73.10 (including under 25s)
If you are assessed as having limited capability for work and work related activity (support group) you get an additional £37.65 = £110.75
There are additional premiums that are paid to those on income related ESA who are in the support group if they get certain rates of DLA or PIP.
The rates are similar under UC except the additional premiums for the most severely disabled claimants have gone.
JSA can also be contributory or income based. Both types pay £73.10/week or £57.90/week if you're under 25. Contributory JSA lasts up to 6 months.