The Baptist Flavor of the Week
Particular baptists are not so called because they are fastidious (though they may be so), rather the term particular refers to the doctrines of particular atonement (commonly called “limited atonement”). The name “particular baptist” makes most sense when you realize that the opposite would be a “general baptist”, or someone who holds to a general or unlimited atonement. The term is synonymous with “reformed baptist” and to some lesser extent “calvinistic baptists”.
Reformed Or Calvinisitc
To many there is little distinction between the terms “reformed” and “calvinistic”. Largely, but not entirely, the distinction is going to be a historic one. The “reformed” baptist will generally view their theology as coming from the heritage of John Smyth and would affirm some historic, baptistic confession. Speaking generally, a “calvinistic baptist” is going to be one who affirms the points of calvinism, but likely is not confessional and probably is happy to associate with modern Baptist history, viewing themselves as having developed their calvinistic theology within the context of the wide-spread general baptist context of modern American Christianity.