Java regex to match these strings

If you don't need to use a regex, then use URI:

private static final Pattern PARAM_SEPARATOR = Pattern.compile("&");
private static final Pattern PATH_MATCHER = Pattern.compile("/file/d/([^/]+)");

// In query parameter...
public static String getKeyQueryParamFromURI(final String input)
{
    final URI uri = URI.create(input);
    final String params = uri.getQuery();
    if (params == null)
        return null;
    for (final String param: PARAM_SEPARATOR.split(input))
        if (param.startsWith("key="))
            return param.substring(4);
    return null;
}

// In path...
public static String getPathMatcherFromURI(final String input)
{
    final URI uri = URI.create(input);
    final String path = uri.getPath();
    if (path == null)
        return null;
    final Matcher m = PATH_MATCHER.matcher(input);
    return m.find() ? m.group(1) : null;
}

Note that unlike a regex, you will receive the result unescaped. If for instance the URI reads key=a%20b, this will return you "a b"!

If you insist on using a regex (why?), then do that instead for the query parameter:

private static final Pattern PATTERN = Pattern.compile("(?<=[?&])key=([^&]+)");

public static String getKeyQueryParamFromURI(final String input)
{
    final Matcher m = PATTERN.matcher(input);
    return m.find() ? m.group(1) : null;
}

But you'll have to unescape the parameter value yourself...

It's prefer for two different regex pattern to split the regex statement and not use |(OR). With using different pattern you will have the first capture group the result you wanted.

Pattern1:

.*key=(.*)=.*

Pattern2:

.*\/file\/?\/(.*)\/.*