Quite recently (in April), Telegram has been banned/blocked in Russia for refusal to give up encryption keys to Russian agencies. Telegram's defence was built around the fact that they don't even have the encryption keys for their end-to-end encrypted secret chats, naturally, and while the ordinary chats are only client-server encrypted, the encryption keys and data are stored in different places under different jurisdictions, as per Pavel Durov's blog post.
WhatsApp, however, uses E2EE by default in all chats, so even WhatsApp servers and anyone else doesn't have access to the messages... unless there's a backdoor, which we can do nothing about, or secret services just use the backups from iCloud/Google Drive (which would give them access to everyone's messages anyway).
So why the selective ban? Is it somehow related to Telegram in particular, or maybe the people behind it?
Telegram is a lot more popular in Russia compared to Whatsapp within the opposition circles. It is used by many people whom the Russian government wants to keep track of, as evidenced by the fact that two factor authentication was added as a response to hacking attempts against Russian activists.
Telegram was founded by an opposition activist Pavel Durov who openly opposes the Russian government.
Telegram itself has declared numerous times that it will not under any circumstances provide message logs from its users to any authorities. WhatsApp is far more neutral in their policies.
China only blocked WhatsApp in September 2017 (Telegram was blocked since the very beginning) so it's possible that Russia will follow up with a ban on WhatsApp too, albeit at a later time.
Quoting Roskomnadzor (i.e. the Internet censorship department) itself:
On the basis of Art. 15.4 of Federal Law No. 149-FZ "On Information, Information Technologies and Information Protection" Roskomnadzor sent a notice to Telegram Messenger Limited about the need to fulfill the responsibilities for communication services.
In accordance with Art. 10.1 of Law No. 149-FZ, these responsibilities are to provide the federal executive body in the field of security (the FSB of Russia) with the information necessary to decode received, transmitted, delivered and (or) processed electronic messages.
The fact that Telegram Messenger Limited did not fulfill the lawful requirements was confirmed by the decision of the justice of the peace in Judicial Section No. 383 of Meshchansky District of Moscow in case No. 5-1794 / 2017 of October 16, 2017, which entered into force on December 12, 2017.
In accordance with Part 1 of Art. 15.4 of Law No. 149-FZ, the above duties must be fulfilled within 15 days from the receipt of this notice.
March 20, 2018
In other words, some "terrorists" purportedly used Telegram to exchange messages and Telegram refused to "collaborate" with the FSB in decrypting those messages. WhatsApp, on the other hand, has not been (yet) held accountable for such "recalcitrance".
The likely real reasons behind the ban have already been nicely explained in the other answer.
I wouldn't go as far as calling Durov an "opposition activist", rather a victim. He's being persecuted by Russian government since 2014, when he refused to hand over data of Ukrainian protesters to Russia's security agencies and block Alexei Navalny's page on VKontakte, an online social network he founded. As a result, he was dismissed as CEO of VK (which he claims was a result of VK being taken over by Putin's allies), left Russia and obtained Saint Kitts and Nevis citizenship.
Since Telegram is also founded by Durov, I suppose the selective Telegram ban in Russia is indeed related to this continued persecution.