'Tool bits' is a common term used for the cutters used in lathes in their most basic form that do the actual cutting. Tool holders usually mean a larger shank tool that carries some type of cutting tool, these days usually disposable carbide inserts. Depending on what kind of tool post configuration you have, you may be limited to regular square section tool bits.... maybe 1/8 or 3/16 or 1/4" square section. I'm only guessing that based on the smaller size of lathe, but you would have to show us more detail. Typically theses are high speed steel (HSS) black like a good drill bit alloy. Or they can be a steel shank with a braze-on carbide tip which comes pre-sharpened. Both are good, there is nothing wrong with HSS & in many hobbyist applications can be advantageous. You do need a simple bench grinder to make to re-sharpen & give you the ability to make different profiles (important!). Any metalworking tooling place will have these blanks but maybe a broader election on-line. Here is a link to KBC (internet order place). Type 'tool bit' in the search engine & that will get you going.
http://www.kbctools.ca/
The picture you are showing is a chuck, but a special one called a pin chuck. If you visualize the body without the pins, that's essentially what the regular chuck looks like at this scale. But before you buy that one, recognize what its designed for according to Sherline. If you are intending this for general machining, it might not be suitable. "
We designed our Pin Jaws specifically for laser engraving rings and other similar parts. These jaws are not designed for machining parts or other uses that require more than finger tight closing pressure to hold the part in the chuck".
Sherline makes nice stuff IMO & the fact that their spindle nose (hopefully) matches your lathe so you can utilize their 3-jaw, 4-jaw & other chucks is great because Unimats are kind of older vintage (60's-80's?) so I'd guess most owners are resorting to ebay scrounging. They were quite unique in their day, but I believe they also had design changes along the way with different models so you have to kind of be aware of that when it comes to buying accessories. Hopefully covered your question.
Personally (you may hate me for saying this) if money were no object & you wanted a lathe of this size, I would go straight to Sherline. They have the most comprehensive set of tooling accessories & it all interchanges with their other stuff like milling machine, rotary table etc. Unfortunately a bit spendy especially with the US$ exchange, but there are good deals on used ones too if you watch.