By process I mean drawn up, sent out (= issued) and collected, i.e. the whole billing process.
NB: "Receipt" is not always the best translation for "comprobante".
For example, in Mexico (and other countries) what we would call an invoice is called a "comprobante fiscal", which is really an invoice for tax purposes. Check out the difference between a receipt and an invoice.

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Note added at 1 hr (2015-08-02 08:27:35 GMT)
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"Girar" has a circular root meaning, depicting the circular nature of the billing cycle.

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Note added at 1 hr (2015-08-02 08:28:55 GMT)
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http://credit.about.com/od/glossary/g/billingcycle.htm

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Note added at 1 hr (2015-08-02 08:30:54 GMT)
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Check out the different types of document in the "comprobantes" section here:
https://www.consulta.sat.gob.mx/SICOFI_WEB/ModuloSituacionFi...

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Note added at 1 hr (2015-08-02 08:37:18 GMT)
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As a result of the above, if the source text is from Spain, I'd usually translate both "recibo" and "comprobante" as "receipt", but my choices might be different in texts from other countries, especially Mexico, which is really in a world of its own.