yes, that is lag, a choppy frame rate is your computer not being able to keep up with the game's graphical requirements.
These are two entirely different issues.
Yes, if the server now has a bunch more graphically intensive things in it, your computer wont be able to run the game as fast, and your frame rate will slow down, but, this is not lag.
Lag is when you click on an NPC and it takes ages for their conversation to come up, or when you type something, hit enter, and it does not appear above your head for some time, or when you click to drink a potion and your character stands there doing nothing for a good while.
The difference between the two is that lag is when you send a signal (click an NPC, type something, click a potion) and it takes times to get to the server and back to you to display it, whereas your computer not being able to run the game at a decent framerate, is when you have done nothing, except perhaps moved the camera angle and the -entire game- slows down.
Your frame rate can be 5000000 frames per second, but if the server is lagging, it would still take time for your character to drink that potion, equally, if the server is lag free but your computer cant run the game at full speed, your character would begin drinking the potion immediately, but your machine would run the animation of the character (and everything else on screen) with many frames skipped out.