Crimea, and Russia's military invasion of it, was something of a special case. It started less than a week after Yanukovych helicoptered out of Ukraine with his vast oil painting collection in hand. The interim government meant to fill the gap until the May elections had just been formed. Ukraine's military had been left rather disorganized after years of corruption in the ranks. Putin knew Ukraine was in zero shape to fight back.
If there was ever a time for Putin to move into Crimea and reclaim what he believed Russia was historically entitled to, this was going to be it. And it was a fairly overt move on Russia's part. Column after column of Russian troops moved off the naval bases and into civilian portions of Crimea. The only thing that was missing was the Russian insignias on their uniforms. Putin rather laughably denied these were Russian troops at the onset of the invasion; however, after the dubious March 16th plebiscite and the subsequent absorption of Crimea into the Russian Federation, Putin went right out and said it: those were Russian troops.
Putin's interest in Crimea goes far beyond NATO and issue of Black Sea ports. Russia already had its naval bases in Crimea, for which the Budapest memorandum allowed. Besides, Russia already had hundreds of miles of coastline along the Black Sea. Just for example, Sochi--the 2014 Winter Olympic host city--was itself a Black Sea port. No, Crimea was most definitely about Putin's imperial worldview: taking back land that the Russian Empire and later Soviet Union once controlled at the height of its power but subsequently lost after 1991.
Putin's view towards Eastern Ukraine is no different than Crimea. In his infamous April 17th remarks, he referred to the region as "Novorossiya", or "New Russia" and claimed that the land was historically Russian. It is widely reported that in 2008, Putin once told Dubya that Ukraine "isn't even a country", with half of it originally belonging to Russia and the rest belonging to other European countries.
Of course, while Putin's view on Crimea and Eastern Ukraine are pretty much the same, circumstances demanded that he approach the two regions differently. In Crimea, Russia was aided by the fact that a majority (although not as overwhelming a majority as Russia implied) of citizens considered themselves to be ethnically Russian. (This was thanks in significant part to decades of policies of Russification of the region, as well as mass deportation of the pre-existing non-Russian populace.) In Eastern Ukraine, while the ethnic Russian population is significant, it is still quite the minority. The majority of persons in eastern Ukraine clearly wanted to remain a part of Ukraine, regardless of any misgivings they might have had about the central government.
Also, the situation in Kyiv had stabilized since late February, meaning that Ukraine might be slightly better equipped to respond to a military invasion (although arguably they'd still be far outmatched.)
So an overt Russian military invasion of Eastern Ukraine like we saw in Crimea wouldn't likely go over as smoothly in Eastern Ukraine. Instead, what we saw was an attempt to transfer the separatist ideology in Crimea over into Eastern Ukraine. One purported Russian FSB agent, Alexander Borodai, actually helped arrange for the Crimean annexation "vote". Once that was done, he immediately went over to Eastern Ukraine, where pro-Russian separatists quickly declared him to be the "People's Prime Minister of Donetsk" (without any vote, of course.)
And what you saw develop in Eastern Ukraine was an undoubtedly pro-Russian separatist movement (they were waiving the Russian tri-colors and chanting Russia's name) fought under the guise of plausible deniability. Many of these armed separatists were locals (mainly those considering themselves as ethnic Russians), but there are likely Russian agents mixed in and giving material support. Consider that the head military leader of the pro-Russian armed separatists is an individual named Igor "Strelkov" Girkin, a former Russian GRU and FSB officer. And considering that the GRU and FSB are the successors to the old KGB, and Putin himself said there is no such thing as a "former" KGB agent, then....well, you draw the line.
Consider also the extremely well armed Vostok Battalion that came waltzing into Eastern Ukraine to fight on the side of the separatists. This force just so coincidentally shares the same name as an infamous force that was fighting on behalf of the Russians to put down the rebellion in Chechnya. When numerous members of the Vostok Battalion were killed in action in Eastern Ukraine, their bodies were all shipped back to Russia.
I think Russia's goal in Eastern Ukraine is to keep the separatists well armed enough with enough covert oversight in the hopes that the Ukrainian army will be worn down and simply gives up its military operation. Leaving Donetsk and Lughansk in enough limbo that eventually they will petition to join the Russian Federation. Meanwhile, during the interim Russia will maintain a level of plausible deniability in its involvement with the separatists. This way, they can avoid the brunt of the much harsher sanctions that would likely be imposed in the event of a formal Russian invasion with the regular Russian army, and avoid the cost of a long, drawn out war to boot.
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