What is the correct command to produce small wedges in differential forms?

As noted in a comment the two symbols are indistinguishable.

When typing differential forms, use the command \wedge since the symbol is called the wedge product. (Similarly when you do wedge sums in topology.)

Use \land when you use the symbol as the "logical and" symbol.

When writing notes in lattice theory I would sometimes also define \newcommand*\meet{\wedge} to give yet another name to the same symbol (and to reflect its name in the theory).

Synonyms can help make your source code more readable.

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See also this question and its answers.

The explanation for the dual naming is in the following lines of plain.tex

837 \mathchardef\wedge="225E \let\land=\wedge
838 \mathchardef\vee="225F \let\lor=\vee

So \land is just an alias for \wedge and similarly for \lor.

LaTeX used to load a slightly modified version of plain.tex; when LaTeX2e was released, the aliases were kept for compatibility reasons in fontmath.ltx:

270 \DeclareMathSymbol{\wedge}{\mathbin}{symbols}{"5E}
271    \let\land=\wedge
272 \DeclareMathSymbol{\vee}{\mathbin}{symbols}{"5F}
273    \let\lor=\vee

(line numbers added for reference).

So what name you use is irrelevant. However, if a package redefines \wedge to point to another symbol, the meaning of \land would be unaffected.