Yes, there are plenty of naming conventions used by the community to identify different groups of different units. I'll list some of them:
- Death Ball: Main Protoss army formed mainly by Zealots, Stalkers, Sentries, Immortals and Colossi. This term was hugely used in both WOL and HOTS since Colossi were the real backbone of Protoss Army. In LOTV, it is not used that much since Colossi and Sentries have been almost cutted of the meta. Some guys still use it to identify an army composed by an high amount of Zealots, Archons, Immortals and Disruptors;
- Chargelots: A group of Zealots upgraded with Charge from the Twilight Council. They are hugely used in mid-late game, expecially vs Terran and Protoss. They can also be very powerful for late harass vs every race;
- Mass Air || Sky Toss: An huge Protoss army formed mainly by air units such as Tempests, Carriers, Oracles (Vision) and, sometimes, a Mothership. It is very popular in PvP. In past, it was mainly used vs Zerg, when Swarmhosts were in meta;
- Blink Stalkers: A mid-great group of Stalkers upgraded with Blink from the Twilight Council. They were really popular in the end of HOTS. They were used to harass or, in certain builds, to all'in against every race, with different approaches;
- Soul Train: A pack of units formed by 2 Immortals, Zealots, Sentries and a Warp Prism. It was hugely used in both WOL and HOTS to identify the famous Immortal 2 Base all'in vs Zerg. Soul train comes to its inventor, @Parting;
- Gate units army: A main army formed by only gateway units. It was hugely used in both HOTS and WOL to identify the famous group of units used in the 7 gateways all'in.
- Speedlings: A bunch of metabolic boost. upgraded zerglings. They are still very popular;
- Cracklings: A bunch of adrenal glands upgraded zerglings;
- Roach + Hydra || Roach + Hydra + Vypers: A combination of upgraded roaches, hydralisks and/or Vypers. It was very popular in HOTS;
- Mass Roach: A main army formed only by roaches. It was very popular in both WOL and HOTS in both ZvP and ZvZ;
- Bling + Mutas: An army formed by Zerglings, Banelings and Mutalisks. It was and it is still used in ZvT vs Bio based armies;
- Bling: An army formed by Zerglings and Banelings;
- Burrowed Roaches: An army or a bunch of Burrow upgraded roaches used to harass in mid-late game;
- Ravagers + Roaches: Army formed by roaches and ravagers. It is really popular in LOTV;
- Ling + Hydra: An army formed by speedlings and hydralisks. It was hugely used in HOTS as a timing in ZvP and now it is used pretty normally against phoenixes openings.
- Bio Army: An army formed by bio units and medivacs;
- Mech army: An Army formed only by mechanical units;
- MMM: An army formed by Marine, Marauders and Medivacs;
- MMM + Widow Mines: Army formed by MMM + Widow Mines. It was very popular in HOTS in TvZ;
- Bio + Siege Tanks: An army formed by Bio units, Medivacs, Tanks and sometimes Vikings;
- Sky Terran: An army formed only by flying units.
General Naming Conventions:
- Turtling: a style of play in which the player plays only defensive until he masses out, 200/200;
- Camper: really similar to Turtling but it is used a lot to identify both Protoss and Terran defensive styles;
- Harassing Drop: A drop made by both Protoss and Terran with Gateway Units or Bio units;
- Harassing units: A bunch units of the same kind used just to harass the opponent. Examples: Chargelots attacking expansions in mid-late game, Speedling and Cracklings, Hellions runby, Widow Mines drops, ...
There are even more conventions, in this moment I don't remember all of them. I'll edit the post when I'll remember others.
If you want to learn even more of those conventions, just lurk on Team Liquid and in main Twitch Sc2 Channels.
I hope I've been helpful.