What you have is an adjustable cup-and-cone style bottom bracket, which was the standard for many decades until cartridges became popular in the '90s. You'll still find cup-and-cone bottom brackets on a lot of bikes, especially at lower price points.

Be sure to remove the outer lockring first, then attempt to unscrew the cup. They can be tight, so use care to keep from damaging the lockring too much. (If you're not using the proper tool, you probably will damage it a little bit.)

And to be sure, the lockring and adjustable cup are removed by turning them counter-clockwise. On the drive side of the bike, the fixed cup is reverse-threaded, so it's removed by turning clockwise. (Unless we're working with an Italian or French bottom bracket, in which case the cups on both sides of the bike are removed by turning counter-clockwise.)