From the Wall Street Journal

With much of New Jersey snowbound in a storm last month, followers of Gov. Chris Christie: “It’s 9 p.m. New Jersey. What’s everyone doing at home tonight?”

Answers poured in, and the responses flowed as if Mr. Christie, a potential contender for the GOP presidential nomination, were texting good friends. Many politicians authorize their aides to manage their social-media accounts, while others, such as Mr. Christie, are intimately involved in their online presence, even if they don’t hit the send button themselves.

Sen. Rand Paul of Kentucky, another potential 2016 hopeful who has built his reputation by drawing policy contrasts with other Republicans, uses Twitter to jab both Democrats and likely GOP rivals. One message on Mr. Paul’s Twitter feed, which has 542,000 followers, criticized Sen. Marco Rubio, a Florida Republican, for “acting like an isolationist” for supporting the Cuba trade embargo. Another tweet poked former Florida Gov. Jeb Bush for supporting the Common Core national education standards, an unpopular stance among many Republicans.

Mr. Bush, who is seeking to build support for an Oval Office bid that is coming nine years after he left the governor’s office, has taken a transactional tone online at times. On Instagram, the photo-sharing site where Mr. Bush has 6,400 followers, there was this plea: “Give us your Instagram name…and I’ll follow you.” (On Twitter, Mr. Bush has more than 161,000 followers.)

In 2012, for the first time, each of the top presidential candidates had a social-media strategy of some sort. Republicans worked hard that year to close the digital gap with Democrats that began in 2008 when then-Sen. Barack Obama first ran for president. In ’08, Mr. Obama successfully engaged with voters online to capture the youth vote, a significant factor in his Democratic primary victory over Hillary Clinton.

Mrs. Clinton, who is widely expected to enter the 2016 contest, maintains no profile on Facebook or Instagram. She first joined Twitter in June 2013 and has sent only eight tweets this year—fewer than Mr. Paul sometimes sends in a day.

Sen. Ted Cruz (R., Texas) is the only potential 2016 presidential contender who has garnered more mentions on Twitter than Mrs. Clinton since the November midterm elections, according to data from Twitter. On Facebook, Mrs. Clinton’s name turns up almost twice as often as any likely GOP presidential candidate, according to data from Facebook.

In her scant Twitter messages, Mrs. Clinton mixes policy with nods to her personal life. A new grandmother, she urged parents to vaccinate their children at a time when Mr. Paul had questioned vaccine safety, with a message on Twitter that said: “The science is clear.” That message—ending with a hashtag, “#GrandmothersKnowBest”—was retweeted nearly 41,000 times, far more than recent tweets by any other White House hopeful.

Candidates have long raised money online, but social media this year appears to be woven in more tightly with the candidates’ day-to-day strategy for positioning themselves in the daily conversation.

Mr. Paul appears to be the first potential presidential candidate who is openly criticizing his would-be rivals on Twitter. In addition to noting Mr. Bush’s support for Common Core, he has criticized Mrs. Clinton’s record as secretary of state, specifically taking her to task for the 2012 deadly attack on the U.S. diplomatic compound in Benghazi, Libya.