What do you mean "both sides"? There's several dozen different major militias, which really if anything fall into three "sides": Assad, Daesh (what you call ISIS), and a loose, sometimes self-sniping (but decreasingly so) alliance of kurds, secular arabs (the nominal FSA), and islamists. All three sides oppose each other.
Russia supports Assad, the party recognized by the UN and human rights groups as responsible for the lion's share of the war deaths and over 10k tortured to death in its intelligence centers. However, it's doing this not by opposing the opposition uniformly, but by heavily focusing on non-Daesh entities. If successful, this would leave a conflict between Assad and Daesh, wherein the west would basically be forced to accept Assad. Iran and Hezbollah are Russia's copatriots in this.
The US and the Gulf states support the non-Daesh forces. The US strongly supports the FSA, would support the Kurds if not for how it would cost them Turkey's support, and is willing to overlook the islamists so long as they continue along their path of denouncing anti-western activity. The Gulf states by contrast have largely been supporting the Islamist militias - Saudi Arabia in particular focusing on Ahrar ash-Sham, while Qatar seems to be in bed with al-Nusra.
Israel wants Assad and Daesh gone, and seems content at sniping at either of them within the Golan Heights, but doesn't seem to want to take a larger, riskier role.
The strategies used by the US and the Gulf states are similar in regards to Daesh: A continuous but restrained bombing campaign. Both the US and the Gulf states take part in this. The arming strategies have somewhat differed, however, and not simply in regards to what groups are the beneficiaries. The US has been very hesitant to deploy weapons to Syria, waiting three years starting and not giving anything heavier than a TOW. The strongest focus has been on coordinating small numbers of FSA members to operate as effective US ground spotters against Daesh. It's not gone very well. Providing intelligence has proven more useful, and the weaponry, although limited, has allowed for more effective operations in certain fronts, such as Idlib. The Gulf states however have focused more on money and arms to their groups, and started it early. The early successes of the islamist militias while the FSA was flailing led to many waves of desertion, turning it from the largest opposition group to at its lowpoint nearly a running joke.
Turkey has proven willing to support taking on Daesh although uses the opportunity to snipe at the Kurds. Turkey's policy of chasing back Syrian planes who even approach their border has created an effective narrow no-fly zone in Syria's north, which militias on the ground have taken advantage of. With Russia's involvement now, however, it's questionable whether Syria will be able to continue that policy, out of fear of hitting Russian jets.
Everyone has their own endgames in mind.
In Russia's and Iran's, the conflict turns into "Assad vs. Daesh", the west reluctantly agrees to accept Assad, wipes out Daesh, and their only Mediterranean ally remains in power. They know he'll probably undertake some serious purges over the next several years while trying to wipe out any vestiges of opposition remaining. Their media will happily not report it.
In the US's and Israel's preferred scenarios, the secular/kurdish/islamist coalition wipes out both Assad and Daesh, with their help on the latter. Each ends up with regions under their control. The goal would be a Lebanon-style power sharing agreement. A more realistic expectation would be a Libya-style post-dictator power vacuum with random sniping militias. Those who support this view that as a vastly better improvement than the current situation or an Assad re-conquest.
In the Gulf states view, they really could care less whether the post-Assad, post-Daesh environment would be a Lebanon-style arrangement or simply another dictator, this time not allied with Iran against them. They'd be quite happy with an Islamist government, so long as it's domestic-focused and has no territorial ambitions.
Turkey will be happy with any situation that doesn't put a force hostile to them in charge and which can disarm or otherwise check the Kurdish militias in the north.
Despite all of the different militias and parties, the conflict really isn't as complicated as it looks. You have Daesh which wants a new multinational caliphate, you have Assad who wants total control over all of Syria, and you have everyone else who doesn't want either Daesh or Assad and are willing to put up with each other to do so. There's only really one irony, and that's how the US and al-Qaeda are basically allies in this. While there's some talk of al-Nusra breaking with Zawahiri (a move that may cost them volunteers but gain them more financial and arms support), as of yet it hasn't happened. al-Nusra is working alongside other islamist militias, the FSA and Kurds, and as of recently the level of infighting has been rather low (though neither the FSA nor Kurds trust them). The weird thing is how much they've been "behaving" themselves (at least by the standards of "totally unregulated militia in a bloody civil war") - there've been abductions and suicide bombings, but also some things totally out of character for al-Qaeda, like apologies when their soldiers kill civilians and nuns complimenting their respectfulness. They don't even impose sharia in all of the towns they control, allowing for the example the Christian towns to continue to govern themselves, which is another weird one. And supposedly this is all on the orders of Zawahiri too. Strange times...