I've read about the color purple being worn by the high class because of its cost and that an emperor marched an army to Briton to gain the seashells to make the dye. I have also read that, to the Romans, the color purple was what we would call crimson red. So did the Romans have our purple and how did they use it?
Here is a thread which should interest you, particularly with regard to how colors were interpreted in antiquity.
The Modern English word "purple" does not mean quite the same thing it meant in antiquity. The Latin word "purpura" (taken from the Greek) does not mean any precise color at all, but any color produced from the dye extracted from the particular mussel you get it from. Pliny actually lists two different kinds of mussels used to make purple, purpura (also called pelagia, or πορφύρα in Greek), and bucinum, which was more common and less expensive. As the OCD notes, the dye produced could be in a range of colors, from a more conventional modern "purple" shade or something more closely approaching indigo to a deep (often very, very dark) red or reddish-violet. Most dyes resulted in redder, darker colors, but there was something of a range, and purple dyes made from different animals were often mixed with each other.
Latin doesn't actually have a word describing the color red, at least not one used particularly frequently. Purpureus is actually the most commonly-used word to describe something that we would say is red--it is even used more commonly than cruentus to describe blood, despite the fact that cruentus literally means "bloody" or "blood-colored." Likewise, there's no specific word to describe our color of "purple," though there are very rare uses of words meaning that something is colored like particular purple flowers (violets and hyacinth come to mind, though both are extremely rare). Now, as I recall, during the Middle Ages the word increasingly became more commonly used to describe a more violet shade, with other words replacing it in its meaning as red, but I don't do etymology or medieval Latin so I may well be mistaken
an emperor marched an army to Briton to gain the seashells to make the dye.
No, this is a garbled version of Caligula's "attempted" assault on Britain. Caligula was likely just going slightly insane by this point. The murex (actually not biologically called murexes anymore) shells that were used in purple dye manufacture don't live in water that cold.
In a very literal sense to your question, yes, but not exactly as you further elucidate.
Caput mortuum violet is a pigment still available today, although it's described as "dried blood". However, the chemistry is different, generally we require light fastness and low toxicity in today's pigments.