The main difference between a Mormon chapel and a temple is that the chapel is open to everyone, while the temple is reserved for those who are practicing members of the Mormon faith. In the chapel, services are held on Sunday, just like in many other religions. Unlike most religions, there is no priest or other paid professional clergy to head the service. The sermons, testimonials, singing and observations of the Sunday sacrament are led by the congregation.
To enter a temple, a person must be in good standing in the faith. This means observing all the rules and principles of Mormonism and reporting to church elders at least every two years. This is where eternal marriages and baptisms are performed. Mormons also practice proxy eternal marriages and baptisms after death, to insure the individuals are "sealed" or forever joined together in the afterlife. Only Mormons of good faith may be married in the temple.
Dress is more casual in the chapels. As long as clothing is modest, it is acceptable, but most men wear suits and ties and women wear skirts or dresses. Temple garments are worn in the temple. Most Mormons wear basic temple garments, which are basically a modified T-shirt and underwear, every day. Regular clothing is worn over it.
The temples have changing rooms where members change into long, white, flowing robes that are worn over the daily temple garments. Everyone wears the same thing, making everyone symbolically equal in the temple. The robes are considered sacred and aren't worn outside the temple.