Not completely, but there is a lot of compatibility.

Filter holders and square/rectangular filters are not all one universal thickness. In practice, though, many 100mm system filters are around 2–3mm thick, and many holders can accept roughly that range. Some holders are modular, so the slot assembly can be adjusted or changed for different filter thicknesses.

A thinner filter will often still work because many holders use spring pressure or pads to grip the filter. The bigger problem is a filter that is thicker than the holder slot was designed for.

The other major compatibility issue is filter size, not just thickness. You need a holder made for the same filter width/format, and you should choose a size that suits your widest lens to avoid vignetting or having to replace the system later.

So no, you usually do not have to buy filters and holders from the same manufacturer, but you should check two things before buying: the filter’s physical size and its thickness range versus the holder’s supported specs.