Anyway, determinate varieties stop growing when fruit sets on the terminal or top bud, ripen all their crop at or near the same time (usually over a 2 week period), and then die. In contrast, indeterminate varieties set new fruits and ripen mature fruits all at the same time throughout the growing season, until frost die the plants.
Semi-determinate var. will produce a main crop that ripens together, but will also continue to produce up until frost. I think you can observe the sequence of fruit sets and ripening to differenciate varieties.
In determinate varieties branches bear flower/inflorescence at the tip and stop growing further, unlike indeterminate varieties keeps on growing bearing fruits on the growing shoot. Determinate ones are short duration, early yielding varieties and indeterminate ones are late, long duration varieties. The varieties having characters in between these two catagories are can be called as semi-determinate.
The definitions to determinate and indeterminate varieties as already given by few of our colleagues hold good. But I feel the concept of semi-determinate tomato is not clearly brought out in these answers.
At field level, determinate tomatoes are characterized by the bushy growth that does not require a support, in normal cases. The height of the plants vary from 30-65 cm depending on the cultivars. Though many books define this growth habit in terms of number of nodes (6-15) it is again genotype specific.
The semi-determinate tomatoes are typical determinate types except in the length of the branches. Since the number of branches are lesser (compared to determinate) and the length of each branch is more, these varieties require the support of a pole of 1 metre lenth, to avoid trailing in the ground. The plant height comes to almost 1-2 metres. Pruning to maintain the apical dominance will not be effective and lead to reduced yields.
When we say, indeterminate, this refers to the varieties that got the capability to grow up to a height of 5-15 metres depending on the genotype and the type of pruning that we adopt. In general, the indeterminate varieties are pruned to a single stem that will grow to continuously to reach the top of the greenhouse, may be up to 10-15 meters. This stem will be supported from the greenhouse roof with twines. Once the shoot tip reaches the roof, the twine will be released gradually so that base of the plant where the harvest is completed will rest on the ground and continuous growth of shoot tip is ensured (process is called lowering).
Simply we can identify determinate varieties if every node branch terminates into flowering and semi determinate if in between one to two internode terminates into flowering.