"Wow, my gosh! What a change! This has never happened before...huh, wait, it's the legend! Goku must have transformed into a Super Saiyan!"
In this form, Goku's irises and pupils are no longer visible, mostly in turn to the power and bleak rage. His body bulks up a little, his hair straightens like that of a Super Saiyan, his skin color also appears to have a yellow hue to it, but there is no considerable change in feature other than a red tint to his hair (due to the reflection of the yellow aura on his black hair, his hair isn't actually red). He gains a yellowish surge of aura, somewhat but not quite resembling that of a normal Super Saiyan's. In turn, the form somewhat resembles a glorified Kaio-ken form and even makes the same sound as it. However, there are notable differences.
When he transformed into the true Super Saiyan during the fight against Frieza, Goku witnessed the murder of his best friend, Krillin (as well as the fact that Krillin isn't likely to be revived with the Dragon Balls, as Shenron had already granted that wish and could not resurrect the same person twice), something that drove him over the edge. This ultimate pain was not fully present during the fight against Slug, that and Goku wasn't at the same power level as when he fought Frieza, which is most likely why Goku did not transform fully. The form of False Super Saiyan was shown to be very erratic, lasting for only as long as the aura is ignited, and using up much more energy to sustain than the full Super Saiyan.
During the battle against Lord Slug, Goku's strength began to quickly debilitate. Having no more options, Goku's anger surged, causing him to gain a massive power increase, enough to quickly overwhelm Slug. However, after a quick sequence of thrashing Slug around, Goku's False Super Saiyan power quickly faded.
One way to put it is that the False Super Saiyan transformation occurs when a Saiyan has the required physical power but lacks the required mental strife to transform into a Super Saiyan. It is apparent however that the form gives a large power increase, enough for Goku, who was being easily beaten by Slug, to quickly overwhelm him.
- King Kai thought this transformation was the Super Saiyan transformation.