Many people think Cyclescheme.co.uk are an official body who manage the Cycle To Work scheme on behalf of the government, they're not. They are a commercial privately owned profit making business, often referred to as a "third party agent" who act as an agent for employers wishing to provide cycles to their staff on the Cycle To Work scheme. They are a "go-between" between the employer and the bike shop, they make their money by charging the bike shop a commission on every bike sale they are involved in. They are not the only agent who do this, there are many of them, however CycleScheme are by far the largest and most successful.
Employers do not need to use these agents to offer bikes to their staff, many don't, preferring to purchase the bike themselves direct from the shop and setup the rental agreements with their staff via their own HR departments. However there is a limited about of paperwork involved in doing that, so many opt to use an agent.
Green Commute are the same as CycleScheme, a commercial business setup to act as a go-between. They also charge a commission to the seller (us).