The typical idea is that several "hits" are required. The difference between proto-oncogene and TSG is mainly in their heritability - TSG mutations are usually recessive (because a heterozygote will still express sufficient suppressor, e.g. p53) whereas proto-oncogenes are dominant (if a consitutively active agent e.g. Ras is present, it doesn't matter if the other allele is under normal control).
A single "hit" in this way (TSG or proto-oncogene) may just cause the cell to die, which isn't a bad thing (in fact, TSG such as p53 often work by inducing apoptosis because proliferative errors make them accumulute). A tumour only results when a single cell accumulates sufficient mutations and genomic damage to gain a reproductive advantage over the cells in its vicinity.
However, you are asking about cancer, which is not simply a tumour. Tumours are any sort of abnormal growth, i.e. neoplasms, but they can be benign! This means they stay in their tumour capsule, do not grow at a fast rate and do not invade or metastasise other tissues. The distinct characteristics that define a cancer are very well-known and were published in a well recognised paper by Weinberg & Hanahan, 2002, "The Hallmarks of Cancer".
The six primary hallmarks of cancer. The first two are the ones most people know, but the other ones are just as essential for
- Independence from external growth signals: Cancer cells produce their on autocrine growth factors or have mutated signal pathways active without GF receptor stimulation (Oncogenes).
- Resistance to anti-growth signals: Cancer cells do not respond to growth-inhibitory factors from outside or inside (Tumour suppressor genes).
- Evasion of apoptosis: Cancer cells resist signals which cause normal cells to die (apoptose) (these are also tumour suppressor genes).
- Limitless replication / Evasion of cell senescence: Apart from stem cells, all normal cells can only replicate their genome a certain number of times before the ends of the chromosomes known as telomeres are too short, disintegrate and cause the cell to enter senescence or die. Cancer cells express telomerase, which extends telomeres and maintains replicative potential.
- Sustained angiogenesis: Tumours and cancers form massive cell heaps. Tumours may stall growth because blood vessels do not grow into the heap and supply the cells with the nutrients needed to proliferate. Cancer cells have found a way to induce blood vessel growth (VEGF) and sustain it in order to maintain nutrient supply.
- Invasion and metastasis: This is the crucial, most distinguishing difference between benign neoplasm (tumour) and malign neoplasm (cancer). Cancer cells degrade the extracellular matrix around them (by secreting metallo-matrix-proteases, MMP), which allows them to move away from where they are and invade into neighbouring tissues. They can also spill into blood vessels this way (especially if the neoplasm is well-vascularised thanks to hallmark number 5), where they can travel to other sites in the body and grow new cancerous tumours in other locations.
There are four more emerging hallmarks and enabling characteristics (immune evasion, inflammation induction, modification of energy metabolism, genomic instability), which allow better cancer growth and make a cancer more dangerous if it acquires them, but these are outside the scope of this answer.