Reaction of Iron(III) with hydroxide ion
I wouldn't expect the reactions to yield different products but rather different particle size. The higher concentrated $\ce{NaOH}$ should hereby produce smaller particles†.

The "solution" in the left vial is probably rather a colloid of microscopically dispersed iron(III) hydroxide. It should show the Tyndall effect if you send a beam of light through it. However, the particles will aggregate over time to form larger particles that also precipitate, as seen in the second image.


† Higher concentration means higher supersaturation. Higher supersaturation leads to a higher nucleation rate, so more and thus smaller crystals are being formed.