A bedsit is a form of accommodation made up of a single unit (typically one room) in a property with shared facilities. The single unit is a bedroom, which may even be en-suite or contain a kitchenette, and is usually rented out to individuals or couples. The occupant of the bedsit will share facilities such as a living room, kitchen, bathroom etc, with other tenants. These other tenants will likely also be occupying other bedsits in the same building.
A house in multiple occupation (HMO) is a legal category of housing and is essentially a residential property rented out by at least 3 people who are not from the same household. A HMO landlord will have more obligations and might need to obtain a HMO licence from their local council. As a result, a HMO property can compromise a number of separate bedsits but bedsits are not automatically part of a HMO.