While there is a lot of overlap when it comes to conifers and evergreens, they are not interchangeable terms. Evergreens are generally just that, ever green. Unlike deciduous trees that drop their leaves when they go dormant in the fall, evergreens keep their leaves year-round. This includes evergreens with needle leaves, like pines and spruces, as well as broadleaf evergreens, such as rhododendrons and hollies. I said they are generally ever green because some plants that remain green in mild climates will drop their leaves in areas with severe winters, for example, several viburnums.
Conifers are plants that produce cones. Many evergreens produce cones, but not all. Broadleaf evergreens, like the rhododendrons and hollies mentioned above, are not conifers. And just to muddle the matter further, there are a few deciduous plants, like larches, that do produce cones.
So bottom line, no, the terms conifer and evergreen are not the same thing.