Both citation builders and managers rely on metadata to create their citations. Metadata is descriptive information about items that is usually hidden in the background, such as in the source code. If an item has good metadata, citation builders and managers will generate perfect, or near perfect, citations. However, poor metadata means poor citations. If information is missing in the metadata, it will be missing in the citation. If there's a typo in the metadata, there will be a typo in the citation. This does not mean don't use builders or managers, it just means that you always need to double check their work.
Example:
Barna, A. & et. al. (2018). EVIDENCE REQUIRED BY HEALTH TECHNOLGY ASSESSMENT AND REIMBURSEMENT BODIES EVALUATING DIAGNOSTIC OR PROGNOSTIC ALGORITHMS THAT INCLUDE OMICS DATA. International Journal of Technology Assessment in Health Care, 34(4), 368-377.
The auto-generated citation above contains two errors due to errors in the metadata: 1) The article title is all caps, and 2) "Technology" is misspelled. These need to be quickly corrected before turning in your paper.
Citation builders are programs that can help you create your citation. In most cases, you simply type in the information the program asks for (author name, title, etc) and hit the submit button. The program will create a citation for you that you can copy and paste into your document. Some builders will autogenerate citations based on just a title or URL. While this can be very helpful, there are sometimes multiple versions of the same resource (such as reprints). Make sure to select the same version of the resource as the one you're actually using.
NCSU Libraries Citation Builder
https://www.lib.ncsu.edu/citationbuilder/
Basic, straightforward citation builder from NCSU Libraries. Covers APA, MLA, and Chicago styles with no ads. Enter the relevant information in the blanks and hit "Submit" - it's that easy!
Cite This For Me
http://www.citethisforme.com/
One of the most popular citation builders. Supports dozens of citation styles including ALA, MPA, Chicago, and Turabian. And while you don't have to watch ads to build citations, this cite is very ad heavy. Does contain limited results for recommended sources that can be expanded with subscription; although, recommended citations usually work or can be expanded on without the need for subscription.
Citation Machine
http://citationmachine.net/
Fill out a form and generate MLA, APA, Chicago and Turabian citations for a variety of common publication types. Ad heavy site that requires you to watch an ad for free 48 hour access past your first citation.
Citation managers are extremely useful tools for any research project. Managers allow you to save resources as you conduct research, allowing you to organize your resources and return to them at a later date. They also generate citations based on available metadata (title, author, etc) and contain plugins that import in-text citations and bibliographies directly into your papers.
Zotero
http://www.zotero.org/
Zotero is a downloadable program that helps you collect, organize, cite, and share your research sources. It allows you to store your content to view later, organize resources into groups and export bibliographies. Zotero's Citation Plugin is compatible with Word, Google Docs, and LibreOffice.
Mendeley
https://www.mendeley.com/reference-management/reference-manager
Downloadable tool that generate citations and bibliographies in a whole range of journal styles with just a few clicks. Mendeley's Citation Plugin is compatible with Word and LibreOffice.
Alden Library at Ohio University gives an excellent introduction to installing and using Zotero.