To steal a bit from an earlier answer of mine - yes, they really did wear hoop skirts. Although the metal versions were probably a minority.

The first skirt supports in western fashion came out of Spain in the late fifteenth century (assuming Norah Waugh's belief that this retable painting does indeed depict early versions is correct) - the verdugado, later transliterated into English as "farthingale". This was a rather cone-shaped hoop formed by applying horizontal channels to a skirt, and stiffening them with reeds or flexible wood. Its transmission from Spain to France, England, and the Low Countries is not clear - there is some assumption that it was brought from Spain to England by the marriage of Catherine of Aragon to Arthur Tudor at the turn of the century, but I can't find anything to back that up, and the earliest French and English portraits that definitely show a woman in a farthingale date to the 1530s, I believe. This portrait of Elizabeth I as a girl ca. 1546 shows the way that the farthingale would hold out the skirt, smooth and flat, for court dress. It continued to be worn in this form for several decades, but in the 1580s certain changes were made to the fashionable French and English silhouette that required a different support. The farthingale in this new form held out the skirt almost horizontally at the hips and then allowed it to fall straight down some distance from the legs, as in this much later portrait of Elizabeth, though when less formally dressed they could wear a smaller "roll" that produced a much subtler (but similar) effect. The full "wheel" farthingale passed rather quickly out of style in the early seventeenth century, with only a small roll potentially continuing to be worn after about 1615; at the same time, the Spanish court reshaped their farthingale into the wide shape we usually associate with portraits of infantas.

Hoops did not come back into fashion until the eighteenth century. Around 1700, some women were wearing heavily starched or glue-stiffened petticoats in order to help hold out their skirts, but by 1710, something rather like the farthingale was back in style. This hooped petticoat was more of a domed shape, and provoked tremendous public comment relating to women taking up too much space on the city streets, flaunting their vanity, etc. etc. In the late 1730s it took on a shape that was flatter in the front and back, but still fairly rounded, which went on to develop into the stereotypical flatness and breadth people often think of when they think of eighteenth-century hoops by about 1750. From there, they became more rounded and narrow by about 1760, and eventually morphed into a bustle situation, with volume at the sides and back, before fading away in the very early nineteenth century.

It should be noted that before the Industrial Revolution, which brought a certain kind of fast fashion to the masses, it was really only wealthy and fashionable women who wore these skirt supports. Where practically everyone in the west could afford a mass-produced cage crinoline in the 1870s, eighteenth-century and earlier women did not wear these, on the whole.

As to whether there's a specific name for the kind of dress you're thinking of ... yes and no. No, because there wasn't a term that meant "all of the dresses that we wear at this point in time", but yes because there were terms for all different types of gowns.

Sacque/Negligée or Robe à la Française - At the beginning of the second half of the century, this was the primary fashionable type of gown for wealthy women. With a fitted bodice front and sides and a back made in free-hanging, unbroken pleats, it made an elegant statement that a woman who wore it could afford several ells more fabric than others and did not do any kind of serious domestic labor. This stopped being worn except in the French court around 1780.

Nightgown or Robe à l'Anglaise - Fitted gowns without the long back pleats were still being worn by most English women, whether in linen or wool for everyday clothes worn by the lower and middle classes, or in silk for a wealthy woman's informal outfit or another woman's best. Around 1780, this once again became the "normal" type of gown for the fashionable.

Polonese or Polonaise - A new type of gown devised in the late 1770s that was cut loosely, so that it didn't fit smoothly down to the waist and then flare out. These had skirts that were cut very round, without corners in the front, and were then tucked up into bunches as in the linked fashion plate. These were typically worn with a pad on the backside, rather than a hoop skirt, as the whole point was to be more casual. A circassienne was a polonaise trimmed with tassels and/or fur, usually cut with short oversleeves - basically, a "Turkish" polonaise.

Chemise gown or chemise à la reine or gaulle - The chemise gown, a loose gown mainly held to the body via drawstrings and sashes, started out as a very exclusive thing worn by Marie Antoinette and her set, but became very popular after the scandal of the queen being painted in it and the painting being displayed publicly.

You can also investigate redingotes, the robe parée, turques, and levites on my blog, if you're interested in more gown types. And if you have any other specific questions, I'd be happy to answer them!