Velux and rooflight are the same conversions. This type of loft conversion is generally very cost effective and does not need planning permission.
A hip to gable loft conversion requires major changes to the roof. A gable wall is built up to the ridge point and a new section of the roof is built to fill in the gap.
A Dormer loft conversion is an extension to the existing roof, allowing for additional floor space and headroom in the loft conversion. Internally a dormer will have a horizontal ceiling and vertical walls compared to the normal diagonal sides of a loft conversion. In attics that have limited space or head height a dormer loft conversion will provide additional space that can make a conversion easier.
A mansard roof has two slopes, the lower slope is close to vertical at 72 degrees and the top section of the roof is almost horizontal. A mansard loft conversion makes a lot more available space within your loft.