Super Saiyan Second Grade (超サイヤ人第2段階 Sūpā Saiya-jin Dai Ni-dankai, lit. "Super Saiyan Stage 2") is the first branch of the advanced Super Saiyan forms, achieved through intense training in the Super Saiyan form. In the form, every nerve is concentrated, sending ki through the body to inflate the muscles, raising both power and speed.
[6] It is a forced increase in the power. It's not that the grade 2 form is "bad" per se, just that Goku realized mastering the standard super saiyan form is better overall. Transforming into the form uses up ki, and even if the stamina isn't as bad as the 3rd grade form, normal super saiyan is still better about it.
Goku's Super Saiyan Grade 1 form in Dragon Ball Z emerged from a moment of righteous fury and was incredibly powerful but drained too much stamina to be sustainable. Vegeta's Super Saiyan Grade 2. Super Saiyan Second Grade, displayed first by Vegeta, has more significant muscle mass and power than the basic form since the saiyan trains to send their ki throughout their body to increase.
Super Saiyan goes through many stages like Super Saiyan Grade 2 and Super Saiyan Grade 3 - not to be confused with Super Saiyan 2 and Super Saiyan 3, which are separate transformations. Both grade 2 and 3 of Super Saiyan, the ascended states of SS, use too much ki, tiring Goku out, which is why he decides not to use them again, and work on another transformation. 4.
Super Saiyan Full Power. It is unclear how this would put Super Saiyan in relation to Goku's regular use of Kaiō-Ken x10 to gain a 10-fold increase in power, and the "up until then" bit muddies things further. An even more advanced variation of the Super Saiyan transformation, which Goku displays to Gohan immediately after showing his son Super Saiyan Grade 2.
The amount of raw power Goku displays in the form leads Gohan to believe that Goku will be able to defeat Cell. Throughout Dragon Ball's story, Goku has achieved many iconic forms, becoming increasingly powerful and leaving certain transformations in the dust. I think Super Saiyan Grade 2 is somewhat stronger than Super Saiyan 2, but it burns off energy at a greater rate and speed isn't increased as much as / proportionally to power since it emphasizes power (but not as much as Super Saiyan Grade 3, obviously), and hence Goku considered regular Super Saiyan (Grade 1) to be best balance-wise; this is why Goku, Vegeta, etc.
use Super Saiyan 2 instead. Goku likely thought that regular Super Saiyan would be more pratical, since the bloodlust can be suppressed more easily. And Grade 4 is also stronger than Grade 2, since it fought pretty evenly with the same Cell that made an utter fool out of Vegeta.