You have it right, catering operations do have some variance between what they offer in terms of services and equipment.
When it comes to venue, some venues provide all the necessary services on site or through their subcontractors. Check to see what they offer. If you are going for a venue that typically does not host gatherings, than little or no other service might be available. Wedding receptions on a beach, in a park, or some other place besides a wedding reception hall usually fit into this category. When this sort of thing happens, it is up to the customer to locate their own caterer and make certain that the caterer and all subcontractors locate the facilities they need. Procuring a kitchen where food can be prepared for a beach or backyard wedding reception can be a significant extra charge. Some caterers require perm ant facilities; others might offer trailer-based operations for cooking food.
In general, the caterer should provide all of the necessary equipment that you order and that goes along with the type of services that they provide. In other words, if you expecting a five course dinner, they should provide the basic plates, silverware, napkins and stemware/barware need for that specific setup. Table dressings such as linens and chair covers might and might not be included, as their use can vary depending on the occasion. A wedding might use elegant tablecloths and chair covers, while a barbecue might use simply table covers and no chair covers. A pure buffet service would likely not include any table linens. Many caterers recognize this and linens could very well be a separate package.
Usually special cooking equipment is not included, but standard kitchen equipment should not garner an extra charge in the majority of cases. If you are having an outdoor grilling picnic, charge for rental of grilling equipment should be expected. Going back to the five course dinner scenario, the caterer should provide, rent, or otherwise obtain the necessary cooking and serving equipment. A charge for something such as a single deck oven (standard kitchen equipment, especially in this industry) should not be expected and you should politely ask your caterer about the presence of such charges. You might and probably should expect to be charged for the rental and use of buffet serving equipment (tables, hotel pans, food warmers, etc.) for buffet service. Also, any décor for buffet tables would likely be an additional and separate charge.
Alcohol service is usually an option and is considered separately from food service by many caterers. Most offer packages classified by time offered, open bar versus cash, exact liquors packages offered, number of servers, types of service, etc.
Entertainment, when caterers do offer it, is always considered a separate matter. I’m not even going to get into all of the options available here so check with your caterer or venue.
In short, venue is very important here. Venues that host gatherings will naturally be more accustomed to offering services to clients. The use by paid permit of the local park, on the other hand, means that you are likely on your own when it comes to your food and entertainment. The exact caterer that you end up working with will have his or her own list of service offered. No two caterers are ever the same and you should check to see exactly what yours offers in terms of services. You also can politely and judiciously inquire as to whether or not you might be able to use your own subcontractors (such as a wedding cake baker or entertainer) if you do not like the options offered by your caterer or host.