Doesn't Start Easily
Has Some Extras

As you suspect the SE was Special edition when you got goodies such as leccy
seats leccy roof and if you were very flush leather, DSE for the diesel
variant and HSE was tagged on when a longer wheelbase version was
introduced, then they changed it a bit ( a lot really ) on the P38 (
possibly country sensitive btw ,I found the US specs)

quote->
As you might expect in a vehicle costing more than $100,000, equipment
levels are quite extensive, even in the base SE model.

Standard occupant safety features across the range include dual front
airbags, front side airbags, front and rear head airbags, anti-submarine
front and rear seats, height adjustable head restraints and three point seat
belts for all seating positions.

Vehicle control features include the permanent four-wheel drive, anti-lock
brakes (ABS), electronic brake force distribution (EBD), emergency brake
assist (EBA), 4-wheel electronic traction control (ETC), cornering brake
control (CBC), dynamic stability control (DSC), hill descent control (HDC)
and engine drag-torque control (EDC).

Comfort and convenience items include climate control airconditioning,
electrically adjustable steering column and front seats, power windows and
mirrors (mirrors also heated), remote central locking, a trip computer with
speed alert and an auto dimming rear view interior mirror. There's an
unusually large number of interior storage compartments, an abundance of
interior lighting and two auxiliary power sockets.

The SE also has a six-speaker single CD stereo system, an immobiliser and an
alarm, alloy wheels (five), front fog lamps and tinted glass.

The HSE models add a memory setting for the driver's seat, exterior mirrors
and steering column; an 11-speaker stereo with multi CD changer and
differently designed alloy wheels.

The top-spec Vogue gets a television and satellite navigation, a tilt and
slide glass sunroof, 19 inch alloy wheels, rain sensing wipers, powerfold
exterior mirrors, bi-Xenon headlamps with wiper/washers, park distance
control, heated seats and steering wheel, and 'Oxford' leather seat trim.

If you are minted ( see also Beckham) the 'autobiography'  when you can have
whatever spec and extras you fancy  at a price.
Overfinch for turbonutter petrolheads ( curly perm optional ) with reworked
suspension 5.7L engine and trim that fits.
and a host of others http://www.rrr.co.uk/P38/Models.htm

and the new shape bread delivery Rangie well they are all HSE except the
limited editions.

Derek
probably missed a load but am I bovvered?