The other two answer already hint at that but maybe one should mention the distinction explicitly:
Apparently the Union of Soviet Socialist Republics (USSR) is a union of Soviet Socialist Republics (SSR), which were prior to joining the union independent socialist countries that organized in the form of soviet republic. While an Autonomous Soviet Socialist Republic (ASSR) is somewhere below a Union Republic, but above an autonomous oblasts and the autonomous okrugs.
So as Alamar has mentioned those are not top-level members of the USSR, but rather nations wihin one of the existing SSRs. What cultural, administrative and political autonomies that actually entailed could vary drastically depending on the era. One important feature of that "autonomous" part however is that these regions can not leave the union on their own, but only as part of their host country. Though if they wish to remain after the independence of their host country they could chose to do that.
Also Crimea's status and history as a region, country, nation and whatnot has changed quite a bit over time. Like ignoring the early history, the Kievan Rus, the Mongol conquest, a Crimean Tatar state that apparently lasted more than 300 years before it was conquered by the Ottoman Empire. The Russian Empire beaten the Ottoman Empire and it became a politically independent Tatar state again but as Russia wanted that Black Sea access they were annexed shortly after. Then the revolution happened and Crimea's status changed wildly:
- Crimean People's Republic December 1917 – January 1918 Crimean Tatar government
- Taurida Soviet Socialist Republic 19 March – 30 April 1918 Bolshevik government
- Ukrainian State May – June 1918
- First Crimean Regional Government 25 June – 25 November 1918 German puppet state under Lipka Tatar General Maciej (Suleyman) Sulkiewicz
- Second Crimean Regional Government November 1918 – April 1919 Anti-Bolshevik government under Crimean Karaite former Kadet member Solomon Krym
- Crimean Socialist Soviet Republic 2 April – June 1919 Bolshevik government
- South Russian Government February – April 1920 Government of White movement's General Anton Denikin
- Government of South Russia April (officially, 16 August) – 16 November 1920 Government of White movement's General Pyotr Wrangel
- Bolshevik revolutionary committee government November 1920 – 18 October 1921 Bolshevik government under Béla Kun (until 20 February 1921), then Mikhail Poliakov
- Crimean Autonomous Socialist Soviet Republic 18 October 1921 – 30 June 1945 Autonomous republic of the Russian SFSR
Then it was conquered by the Nazis in WWII and after the Soviet Union regained control over the territory they deported the Tartars elsewhere within the USSR so that they can demote Crimea from an ASSR to an oblast within the Russian Soviet Federative Socialist Republic (RSFSR). Which then was in 1954 was transferred to the Ukrainian SSR on the 300th anniversary of a union of Russia and Ukraine:
The territory had been recognized within the Soviet Union as having "close ties" to the Ukrainian SSR, and the transfer commemorated the Union of Russia and Ukraine Tercentenary. Wiki
Also apparently Stalin's successor Nikita Khrushchev was from Ukraine. And it remained an Oblast of Ukraine until 1991. However when the RSFSR and the Ukrainian SSR left the Union, the Crimean Oblast asked for the restoration of it's ASSR status which is the subject of that referendum and also for a Union Republic status within the New Union Treaty. Which, if it would have that had come to exist, would have meant that Crimea would have been an independent country separate from Ukraine.
So Crimea didn't so much join Ukraine but remained within Ukraine. Also that's too simplistic as well. As the Crimean ASSR then transformed into the Republic of Crimea, which actually declare it's independence as a sovereign country, but a day later specified for that state to be in a union between Crimea and Ukraine as basically a federation of 2. Scheduling a referendum which Ukraine was not too fond of and which never actually happened and so they struggled for some years to figure out their exact status and relation to each other.
With apparently a noteworthy encounter in 1995 when a pro-Russian president was elected in Crimea who received a boost from a referendum for more autonomy, yet who managed to run into conflict with the Crimean parliament, who then downgraded him from head of state to head of the executive branch, upon which that president disbanded parliament and apparently attempting a power grab. Upon which Ukraine intervened, appointed a new president, abolished the constitution and the laws in conflict with the Ukrainian constitution, downgraded the status of Crimea and put the former president on a plane to Moscow.
And after period of full control by Kyiv Crimea again became an Autonomous Republic and got a new constitution in 1998.
Meanwhile after the fall of the Soviet Union, Russia decided that the 1954 transfer was a mistake and also wanted Crimea back though that apparently was settled for some time with a special status for the city of Sevastopol and the Black Sea Fleet and affirmed the lack of a claim of Crimea and the territorial integrity of Ukraine (including Crimea) in the Budapest Memorandum of 1994.
So yeah the relation of Crimea, Russia and Ukraine and it's status as independent, associated, incorporated, dependent, occupied, self-governed and whatnot is quite complicated. Though with all the quests for independence and autonomy it's quite odd that within Russia, Crimea currently doesn't even have the status of an Oblast anymore but was downgraded to a part of the southern district.