Two different problems get called lag. Network delay means your actions take too long to reach the server; low frame rate means your own machine cannot draw fast enough. The fixes have nothing in common.
The distinction is visible once you know what to look for. Low frame rate makes movement look choppy even in menus and single-player; network delay leaves the picture smooth while other players teleport and hits do not register.
Most games can display both figures on screen. Frames per second describes rendering; ping and packet loss describe the network.
Packet loss deserves separate attention: a low ping with occasional loss produces worse gameplay than a consistently higher ping.