The "external exposure" therapy is the most frequently used modality. It uses the external beam of various types of radiation.
Unlike photons (i.e., X-rays and gamma-rays), protons and heavy ions have Bragg peak (rise in the dose deposition at the certain depth) with benefits to deep-seated tumors. In addition to conventional photons, there are more recently developed photon modalities with the improved dose conformity, such as IMRT (intensity modulated radiation therapy) and IGRT (image guided radiation therapy).
The biological effectiveness also differs amongst types of radiation. The effectiveness of protons is somewhat similar to that of photons, but heavy ions are more effective than photons. Heavy ions sometimes make hypofractionated therapy possible and are effective for photon-refractory tumors.
The "internal exposure" therapy can be broadly divided into two modalities. One uses the sealed radiopharmaceutical source, whilst the other uses the unsealed source.
The internal exposure therapy using the sealed source is called "brachytherapy". "Brachytherapy" can be further divided into "interstitial brachytherapy" (typically applied to head and neck cancer and prostate cancer) and "intracavity brachytherapy" (typically applied to esophageal cancer and cervical cancer). Moreover, high dose rate or low dose rate is used for "interstitial brachytherapy".
The internal exposure therapy using the unsealed source somewhat belongs to the "systemic exposure" therapy, where the source is administered intravenously or perorally. Some nuclides preferentially accumulate in certain tissue (e.g., iodines to thyroid), but others distribute more systematically (e.g., strontium). The typical example is the use of 131I for thyroid cancer (also hyperthyroidism).
The "systemic (external) radiation" therapy includes total body irradiation (TBI) or whole body irradiation (WBI) with photons to eradicate leukemia and prevent graft versus host disease and total skin irradiation with electrons to treat mycosis fungoides.
As mentioned above, the "systemic (internal) radiation" therapy includes the use of the unsealed radiopharmaceutical source that does not accumulate in specific organs/tissues such as strontium.
Every cancer has its best treatment approach using either External Beam Radiotherapy EBRT), Brachytherapy (internal radiation) or a combination of both. The basic idea is to deliver radiotherapy safely such that tumor get planned dose and the surrounding normal tissues are spared. It is beyond the realms of this 'answer' to describe it in each cancer. The best way will be to see the NCCN guidelines. I'll give you an example of carcinoma cervix, where patients are treated with a combination of EBRT and brachytherapy to bring the total dose of 70-85 Gy. But for very small tumors, brachytherapy is sufficient. Radiation is rarely given 'systemically', except in very low dose in skin lymphoma (mycoises fungoides) or as total body irradiation in bone marrow transplant protocols. Hope the answer helps. Again, it is beyond the scope of this 'answer' to describe it in details.