According to the on-line help for ArcGIS https://desktop.arcgis.com/en/arcmap/10.3/manage-data/raster-and-images/curvature-function.htm
curvature units are given in hundreths of z-units (1/100). In this documentation there appear profile curvature, planform curvature and standard curvature. The first two of them are the curvatures along and across the maximum slope direction. It is not clear what standard curvature means but probably it is the result of a convolution with a Laplacian filter.
Saga documentation is more precise: http://www.saga-gis.org/saga_tool_doc/2.2.3/ta_morphometry_0.html
The Curvature function displays the shape or curvature of the slope. A part of a surface can be concave or convex; you can tell that by looking at the curvature value. The curvature is calculated by computing the second derivative of the surface.
The Profile curvature is parallel to the slope and indicates the direction of maximum slope. It affects the acceleration and deceleration of flow across the surface. A negative value (A) indicates that the surface is upwardly convex at that cell, and flow will be decelerated. A positive profile (B) indicates that the surface is upwardly concave at that cell, and the flow will be accelerated. A value of zero indicates that the surface is linear (C).
The different optional parameter is there while choosing curvature, make sure what you are selecting and what is the algorithm you are choosing of it. I think you are choosing the first option General curvature. If you can choose Profile curvature, then maybe you get similar value that of ArcGIS. Try other curvatures and check the unit of too.
These are the different algorithms
Available Choices: [0] maximum slope (Travis et al. 1975) [1] maximum triangle slope (Tarboton 1997) [2] least-squares fitted plane (Horn 1981, Costa-Cabral & Burgess 1996) [3] 6 parameter 2nd order polynomial (Evans 1979) [4] 6 parameter 2nd order polynomial (Heerdegen & Beran 1982) [5] 6 parameter 2nd order polynomial (Bauer, Rohdenburg, Bork 1985) [6] 9 parameter 2nd order polynomial (Zevenbergen & Thorne 1987) [7] 10 parameter 3rd order polynomial (Haralick 1983) Default: 6
Saga gis has several method to calculate curvature. Zevebergen and thorn method is good. i dont know which method has been used in Arcgis. But Saga gis method is better.
may be arcgis use 8 neibours cell for calculation just arcgis pro has mor than 3*3 windows size for calculation. and Saga gis use more cells to calculation.