You may find this comment by /u/etan-tan helpful.

There are four main reasons, 1) the summer 1944 offensive could not achieve the breakthrough it sought and a consequent total defeat of the Finnish army before all available Soviet reinforcements were needed in the more urgent race to Berlin; 2) the Soviet foreign policy aims were achieved without having to occupy or coup Finland, whereas making a satellite out of Finland would've almost certainly caused Sweden to declare for the Western allies and, later, NATO; 3) the U.S. (and to a lesser extent, British) considered that Finland had been drawn to the war she didn't want and consequently should be permitted to choose its post-war government, unlike Hungary for instance; and 4) Finnish communists were unwilling and unable to take power in a way they did in Czechoslovakia for instance.

First, probably the decisive difference was that the Finnish army was never crushed the way Hungarian armies, for instance, were. While the Soviet summer 1944 offensive caught the army largely unawares and initially achieved considerable gains, resistance, reinforced by German troops and weapons, stiffened considerably. Soviet efforts to achieve a breakthrough that would've permitted them to advance towards Helsinki, as the Soviet high command had ordered, failed and the offensive stalled. By that time, Operation Bagration against the Germans was well under way, and the Soviets were notoriously loath to reinforce stalled efforts. Hence, reinforcements that had been reserved for exploitation of a breakthrough against Finland, and subsequent occupation, were sent to fight the Germans instead. The intensity of the fighting most probably had an effect as well: both Stalin and Molotov remarked later that based on their experience, occupying Finland would’ve only created “a festering sore” that would’ve been costly to pacify.

Second, the offensive nevertheless helped to knock Finland out of the war, while its defeat led the Soviets to moderate their demands. Finnish government had been exploring a way out from the war since Stalingrad, and peace feelers had been made in early 1944. However, the Soviet demands at that time would’ve meant a de facto occupation. After the defeat of the summer offensive, the terms, while still harsh, did permit a measure of independence. For the Soviets, the end of hostilities achieved the strategic aim of knocking Finland out, to be dealt with later if necessary, and ultimately gave them the objectives Stalin had sought with the Winter War, namely, a border farther away from Leningrad and a military base in Hanko peninsula EDIT: Of course in Porkkala, close by though. Especially after the war, it became pretty clear to everyone that it was more useful for the Soviets not to occupy Finland, as doing so would’ve certainly led to the Swedes to declare for NATO. Keeping Sweden - which, for instance, had the fourth largest air force in the world at one point - at least nominally neutral was more beneficial for the Soviet position than overt occupation of Finland would’ve been. Finland did not endanger the Soviet Union in any manner, it’s independence was circumscribed and the Friendship, Cooperation, and Mutual Assistance (FCMA) Treaty essentially made Finland a silent if very unreliable member of the Warsaw Pact in case of hostilities between NATO and the Soviet Union.

Third, the opinion of the U.S. government in particular was that Finland had been forced into the war against her own will - that is, without Soviet attack she would’ve remained neutral - and therefore she should be allowed to choose her own post-war government. Stalin would’ve obviously wiped his arse with these considerations if the Soviet breakthrough had succeeded, but it did not, and at least as long as the Soviets were fighting Germans and receiving Lend-Lease aid, the opinions of the U.S. government had some weight. Post-war, the U.S. government considered Finland a lost case until about 1949, when it became clear that a communist takeover wasn’t imminent; afterwards, Finland became a scene of a hearts and minds struggle between the US and Great Britain on one hand, and the Soviet Union on the other.

Fourth, possibly partly because of the reason above, the Soviets were unwilling to actively help Finnish communists to power, although they also made clear that they could help the communists to retain power if they first gained it themselves. This was not to be, however, and despite a major electoral victory for the left in the first post-war elections, the Communist Party of Finland never really managed to get its act together enough to mount a coup in Czechoslovakian style - even though this was certainly a threat.

The general opinion among Finnish historians is that reasons 1 and 2 were the most important factors that prevented Finland from being made a satellite state or even annexed into the Soviet Union outright, like the Baltic states were. If occupation would’ve been the only way for the Soviets to achieve their foreign policy goals, it would’ve certainly happened, despite any reservations. But since it wasn’t, occupation would’ve been a waste of resources and probably disadvantageous in the terms of balance of power, due to the inevitable Swedish reaction.