Tomatoes are typically divided between heirloom and hybrid tomatoes, but they can also be further categorized into determinate vs. indeterminate types.
Determinate tomatoes, also known as bush tomatoes, are generally smaller plants, growing more compact and finite. This makes them great for growing on a patio or in a garden with limited space.
Determinate tomatoes also have shorter harvest times and bear fruit all at once, making them great for cold climates and for making sauces, soups, paste, and other canned products.
Indeterminate tomatoes, also known as vining tomatoes, will grow indefinitely if unpruned and produce fruit for an entire season before being killed by frost. This makes indeterminate tomatoes great for slicing on salads and burgers.
Determinate tomatoes usually grow to no more than 3-5 feet (0.9-0.5 m) and tend to develop into a compact bush. They are easy to grow for beginners, require minimal pruning or staking, and grow great in containers or grow bags.
Determinate tomatoes are also perfect for cold climates, as they produce their entire harvest within a 3-week period, usually in about 60-70 days vs. 70-85 days for indeterminate varieties.
Never prune the top branch (only prune the lowest branches if necessary) of determinate tomatoes, as this will stop growth and limit fruit production. Fruit production usually ends when flowers set at the very top branch of the plant.
Popular determinate cultivars include Patio, San Marzano, Better Bush, Celebrity, Rutgers or Jersey, Green Zebra, Plum Regal, Gold Nugget, etc. 
Indeterminate tomatoes have the capacity to continue developing branches, even after flowering. This branching can occur indefinitely, so indeterminate tomatoes tend to grow into taller, leggier plants.
With the right support (e.g. staking, trellising, caging, etc.), some tomato plants can develop into what resemble trees towering 20-30 feet (6-9 m) tall.
These plants can also produce up to several hundred pounds of tomatoes per plant.
To maximize yields and direct some energy back to fruiting, indeterminate tomatoes should be pruned occasionally.
To prune, remove undesired suckers at the point where they attach to the main stems. Young suckers can be pinched off with your hands without leaving too much of a scar.
Popular vining tomatoes include Black Cherry, Big Beef, Early Girl, Cherokee Purple, Brandywine, Juliet, Big Rainbow, Amish Paste, Cherry Roma, Jet Star, among many others.
Bush vs Vining Tomatoes
Vining and bush tomatoes are just other terms for indeterminate (i.e. vining) vs. determinate (i.e. bush) tomatoes. Vining tomatoes need to be pruned, caged, staked, or trellised to maximize yields and to control the indefinite growth. Bush tomatoes grow compact, require minimal pruning, and make great container plants.
Rarer semi-determinate varieties also exist, and they do not fall neatly into vining or bushing types. These semi-determinate types tend to grow taller, but still produce compact bush-shape plants. However, they also frequently produce a second harvest crop after the first, though they will not grow indefinitely like indeterminates.
 Schoenwandt, R. (2019, May 29). Determinate or Indeterminate—Choosing the Best Tomato for You and Your Garden. UCCE Master Gardeners of El Dorado County. https://ucanr.edu/sites/EDC_Master_Gardeners/files/305005.pdf.
 LeHoullier, C. (2014). Epic Tomatoes: How to Select and Grow the Best Varieties of All Time. Storey Publishing, LLC.