There are various plagiarism checkers, and some of them are as full-fledged as Turnitin and even more cost-effective.
For schools, it is better when a plagiarism detector has its own Moodle plugin, which facilitates checking the assignments. For instance, a school can organize special folders for students where separate assignments and plagiarism reports on different subjects can be stored. Your teachers set the number of attempts for plagiarism detection until you upload a final version of your essay. When the text is scanned through a plagiarism detector, you will see from 0 to 100% of coincidence. Such checkers have been programmed to scan through web resources and databases, as well as the institution's Storage (it can consist of school archives of previously written works and research papers). Other alternative plagiarism checkers include Grammarly, Paper Rater, PlagiarismSearch, Unicheck, PlagScan, Plagramme, DupliChecker, Copyscape, Plagiarismhunt, WhiteSmoke, among others.
All those checkers have free versions, but their premium or customized accounts offer you more features, and some of them can be even tailored precisely to your needs. For instance, PlagiarismSearch allows you to choose the exact number of words to check within the desired time frame (but this option can only be customized: you will not see it on the website). I use most of the mentioned plagiarism detectors as a content writer, but I can also scan my own prose and poetry through those tools just for fun. Some strange contextual coincidences can be found. Well, "there is no new thing under the sun" until you invent your own linguistics and new meanings.