definitely server lag.
I would imagine that the mods installed are probably causing tick overload from the local hosted server if you are in singleplayer.
Minecraft has two forms of lag: framelag, which is obvious from f3 diagnostics in top left, and then server lag which becomes more obvious the higher is becomes due to desync on player actions.
Frame lag is cause by any number of things, mainly from gpu rendering not being powerful enough.
Server lag is a hard one to treat because it mainly comes from having too many operations happening between server calculations. This is especially hard on processors because minecraft only runs servers on a single thread, so you seriously need to pump out high clock speed. What happens when your client does something and there is server (tick) lag, is that your client will show things operating normally, but the server is still backed up calculating everything from before, leading to exactly what you see there: a block being mined and then dropping a second later.
Only way to fix your issue is to put less load on the server, either by removing mods, using less machines, or giving it a more powerful (higher clock speed) cpu.
As a side note: it isn't that uncommon for minecraft to eat all the RAM from your memory causing minecraft to chug. If you are using a launcher, check it's settings and look for a way to raise the memory allocated to java. Just remember, minecraft will eat every last bit, so if you give it too much, your OS will chug instead.
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HiradeGirl:
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NinStar:
