I found mini winglets just in B 737-200. What's the differences between mini winglets and the blended ones which Boeing uses in more recent versions? (picture source)
The one above starts at 0.4x chord from the leading edge. For a test program on KC-135 tanker, which I suppose was first application of the winglets, they used the type of winglets shown in the question:
Conceptually there is no difference in the "mini-winglets" and the "Blended winglets" While I think almost all the wingtip shapes are more or less of same efficacy, I can think of couple of reasons for variations seen among various aircrafts - One is patents taken for some shapes would force other OEMs to come up with different shapes. Second is weight of the wingtip vis-à-vis the reduction in fuel burn. Typically winglets reduce fuel burn by ~3-8% but in some cases, the increased weight can off-set majority of the fuel burn or even prove to be more than compensating for it, especially on shorter hauls. One may be able to make a lighter blended winglet using co-bonded, co-cured composite structure as compared to the short winglet mentioned in the picture which with say bolted joints might end up heavier. I think it would be difficult to say make any generalised comment on this.
Adding winglets to an existing design puts stresses on the existing spar ends that they weren't designed for. Fortunately, they're stronger than may be necessary at the ends due to mechanical implementation requirements, allowing some additional load. But a "full size" blended winglet should be designed in from the start to ensure sufficient strength, minimal weight and avoidance of aeroelasticity (flutter).
Boeing 737-200s are comparatively old and the winglets developed for them are not by Boeing, but by a third party, as noted by b737.org.uk:
... 737-200..., fitted with mini-winglets. This is part of the Quiet Wing Corp flap modification kit which gained its FAA certification in 2005.
The other types of winglets in B737s- blended wing winglets in 737-800s, the AT winglets in 737 MAX and Split Scimitar in NG 737 (through there is some overlap here) were all developed by Boeing (with others) and are available from production units and also as retrofit.