Hi there wstkygirl,
Yes quite true, there are many what we call 'the red and purples' a lot of them being very popular in the early 1900's because they were recognised as 'good strong growers' and a lot being hardy in zone 8 +.

It is very difficult to tell the difference between some of them without having one of each, sometimes it's just a question of the veining in the sepals(upper petals) and corolla (lower petals or sometimes referred to as 'skirt' in large doubles.

So let's try to distinguish between Dollar Princess and Royal Velvet.
Personally from your photo (taking into consideration that photo colours are not always the 'exact' colours), I would say you have Royal Velvet. But you had better check the two comparisons below.

ROYAL VELVET
The tube,(above the sepals) is medium length and crimson.
The sepals, are short and broad, held well out over the corolla, also crimson.
The corolla, deep purple, the outer petals splashed with crimson. The blooms are very full, fluffy and of medium to large size.
The foliage, medium green finely serrated edges to the leaves.

DOLLAR PRINCESS.
Tube, small cerise.
Sepals, cerise, quite broad and reflex (turned upwards) almost to the tube.
Corolla, purple with cerise at the base of the petals.
Foliage, medium to darker green and serrated.

As you see from the two descriptions Dollar Princess has more of a pinky red markings(cerise) whereas Royal Velvet is a more red markings(crimson)

Royal Velvet would be ideal in a container, place it in a position where it does not have the hot pm sun on it. Water in the mornings. Feed a quarter strength balanced feed NPK 20-20-20 everywatering. Keep moist, not soaking wet. Hope this helps you Kath:)

Thanks!!!