When you report what someone else said or thought, or even what you yourself thought or imagined, if you do not use a direct quotation of the words, then you are using indirect discourse. This kind of report never promises, although it often seems, to report precisely the words that were said. There are different rules for the various ways we talk, think, sense, and know.
Statements are reported in English with "that": "I said that ..." In Latin with the accusative - infinitive phrase.
Questions are reported in English with a simple interrogative; in Latin the verb after the interrogative must be in the subjunctive.
Orders (including persuasion, suggestion, urging) are reported in English with the infinitive: "I order you to do it." or with that "I suggested that he do this." In Latin, you use what is called a jussive noun clause.
Fears in English are reported with a noun clause introduced with "that"; in Latin they use a fearing clause introduced with "lest".