Are the Middle Ages the same as the stone ages?

No.

Let me expand that a bit.

The "stone age" is the period before people learned to work metal. There are a number of division and subdivision as various technologies developed, but in general it means, at least in the context of Europe, before 5500 BCE.

The Middle Ages are much later. It can refer in general to anytime from the collapse of the classical civilizations of the ancient world in Europe, through the start of the renaissance. There are different interpretations as to where exactly to draw the line, some date it from the fall of rome in 410 CE, others to 500 CE. Very roughly the middle ages last until 1500 CE, although the Renaissance was underway in parts of Europe before that.

The early middle ages, sometimes called the Dark Ages, are from the start of the middle ages,where ever you date that, to about the year 1000. This is a period of decreased population, diminished city life, decay and almost end of long distance trade and money economy, and a nearly total loss of literacy outside of the church.

There is something of a reboot around the year 1000, and things start to improve. Very gradually, cities grow, the economy improve, a merchant and urban class begins to develop. The period from 1000 to about 1200CE is known as the Central Middle Ages,

The period from 1200 to 1500 is what most people think of when they hear "middle ages". This is the age of armored knights, chivalry, Chaucer, the medieval romances, the great Cathedrals, it is the setting of stories like Robin Hood and Ivanhoe. While still an agrarian society with a low literacy rate, this period has a vibrant urban culture, art, literature, and architecture we still consider inspirational. There is also a solid money economy with long distance trade. This period is called the "High Middle Ages".