Numeric, author-year, journal styles

A citation style controls two things: what the in-text marker looks like, such as [12] versus (Knuth, 1984), and how each entry in the reference list is formatted. The good news is that the style is completely separate from your .bib database. You can switch a paper from numeric to author-year, or reformat it for a different journal, by changing one line in the preamble. Your entries never need to be rewritten.

Changing style with classic BibTeX

With BibTeX, the style lives in the \bibliographystyle{...} command, which names a .bst file. Swap the argument and recompile:

\bibliographystyle{plain}    % [1], entries sorted alphabetically
\bibliographystyle{abbrv}    % like plain, but first names and journals abbreviated
\bibliographystyle{alpha}    % labels like [Knu84] built from author and year
\bibliographystyle{ieeetr}   % IEEE-style numeric, in citation order
\bibliographystyle{apalike}  % author-year, needs \usepackage{apalike} or natbib

Journals and conferences usually ship their own .bst file, for example IEEEtran.bst or ACM-Reference-Format.bst. Put that file next to your main.tex and name it in \bibliographystyle. Note that a .bst bakes in one look; if the venue wants author-year cites, you also need the natbib package to get commands like \citep and \citet.

Changing style with biblatex

With biblatex, the style is an option on the package itself:

\usepackage[style=authoryear]{biblatex}

Other common values are style=numeric, style=numeric-comp for compressed ranges like [3-6], style=alphabetic, and style=apa or style=ieee from add-on packages. Because biblatex styles are written in LaTeX rather than the old .bst language, they are far easier to tweak, for instance to change punctuation or drop URLs.

Recompile properly after switching

After any style change, the old auxiliary files still contain data formatted by the previous style, so run a full cycle: compile once, run the backend (bibtex for classic BibTeX, biber for biblatex), then compile twice more so cross-references settle. Oleafly runs this cycle for you, but if citations look stale after a manual switch, deleting the .aux and .bbl files and rebuilding from scratch clears it up.

Which family should you use?

If the target venue provides a .bst file or a class that expects BibTeX, use classic BibTeX; that is still the situation at most journals. If you control the format yourself, as in a thesis or a preprint, biblatex is the more capable choice. The trade-offs are covered in Classic BibTeX or biblatex, and the command differences in natbib habits vs biblatex commands.