Haha I work with manufacturers in the food industry and believe me people dont want to know what it takes to get a product on a grocery shelf. Tallow is basically refined beef fat and lard is pig fat. The "by-products" from slaughterhouses and processing plants are processed to separate the tissue,bone,fat etc through various process to be used in other areas and one being beef tallow for food production or soap manufacturing.

Textbook as follows:
Industrial rendering is a factory-scale process that uses slaughterhouse waste, restaurant grease, and butcher shop trimmings as its raw materials. This material can include the fatty tissue, heads, bones, offal, other waste animal parts, animals condemned at slaughterhouses, and those that have died on farms, in transit, etc. The raw material may be beef, pork, or poultry. The rendering process simultaneously dries the material and separates the fat from the bone and protein. After rendering, the materials are much more resistant to spoiling. The fat can be used in animal feed, in soap-making, in candles, as a raw material for biodiesel production, and as a feed-stock for the oleochemical industry. The bone and protein becomes dry particles known as meat and bone meal. For many years meat and bone meal were fed to cattle. This practice is now prohibited in developed countries because it is believed to be the main route for the spread of BSE (mad-cow disease). Meat and bone meal is still fed to non-ruminant animals in the United States.

Edible rendering processes are basically meat processing operations and produce lard or edible tallow for use in food products. Edible rendering is generally carried out in a continuous process at low temperature (less than the boiling point of water). Basically the process usually consists of finely chopping the edible fat materials (generally fat trimmings from meat cuts), heating them with or without added steam, and then carrying out two or more stages of centrifugal separation. The first stage separates the liquid consisting of mingled water and fat from the solids, and the second stage further separates the fat from the water. The solids may be used in food products, pet foods, etc, depening on the original materials. The separated fat may be used in food products, or if in surplus, it may be diverted to soapmaking operations. Most edible rendering is done by meat packing or processing companies.

Materials that for esthetic or sanitary reasons are not suitable for human food are the feedstocks for inedible rendering processes. Much of the inedible raw material is rendered using the "dry" method. This may be a batch or a continuous process by which the material is heated in a steam jacketed vessel to drive off the moisture and simultaneously release the fat from the fat cells. The material is first ground, then heated to release the fat and drive off the moisture, percolated to drain off the free fat, and then more fat is pressed out of the solids which at this stage are called "cracklings" or "dry-rendered tankage". The cracklings are further ground to make meat and bone meal. A variation on a dry process involves finely chopping the material, fluidizing it with hot fat, and then evaporating the mixture in one or more evaporator stages. Some inedible rendering is done using a wet process, which is generally a continuous process similar in some ways to that used for edible materials. The material is heated with added steam and then pressed to remove a water-fat mixture which is then separated into fat, water and fine solids by stages of centrifuging and/or evaporation. The solids from the press are dried and then ground into meat and bone meal. Most independent renderers process only inedible material.