TL;DR at bottom again.

Not quite, though one could argue the result is the same for basic tasks. Plants have no muscle or nerve system in a traditional sense. Plants use their cell walls to do this, which animal cells lack, possessing only a membrane.

The responses to stimuli and ion flow in a plant happen on a cell to cell basis, though cells can communicate through tunnels in their cell walls, known as plasmodesmata, and I'm sure you could find studies where hormones diffuse into neighboring cells.

Muscles move by having ropes of cells packed very thickly together, and shorten or lengthening by having millions of microscopic hands working together to pull along/against surrounding muscle cells (this is a layman's allegory, if you want a more in-depth look, search cross-bridge cycling in muscular tissue). Plants, as stated before, rely on water pressure in cells to flex their wall filaments in certain directions, more akin to how hydraulics work.

TL;DR: Plants do not have muscles or nerves, but can appear to accomplish tasks in a different manner.