Introduction
Memory-map ®, Fugawi ® and OziExplorer ® each have their own file format for saving maps. they also offer the ability to read raster images of maps in the graphic file format TIFF, JPG and PNG with a color depth of 256 colors (8 bit).
Differences and similarities between TIFF, JPG and PNG
For all technical differences between the formats I invite you to see for yourself in the Wikipedia. All three formats have an option to compress graphics files, each in their own way. TIFF and PNG do it in a non-destructive way. There is no information lost while compressing. JPG does the compression in a non-reversible destructive way. The quality of the map can be compromised (blurrier). The advantage of the JPG format: the size of the file is normally (much) smaller than TIFF and PNG. The difference between TIFF and PNG is the way a file is compressed. PNG files are usually smaller. TIFF and JPG are more usual. It is a choice. Personally I prefer PNG.
Converting to a color depth of 256 colors
There are several methods for converting. Most graphics programs have options on board. You can also choose a picture viewer or picture organizer. These programs have often also a possibility to convert graphic files. Finally, you can use a special conversion program.
When converting to 256 colors color difference can occur (for example, a green or a blue cast). This is a consequence of the (mathematical) method used for converting. May be there is an option in the program you use to to adjust this (Search under preferences/settings). Isn't the the case just find another program.
A last resort is to convert the file to the GIF format (native 256 colors) and proceed to convert once again to the desired file format
The method you choose is personal. I have good experiences with the programs XnViewMP® and Paint.Net®.
If storage space becomes tight
If the storage space for files becomes tight, there is little a trick. The various graphics programs have the ability to limit the number of colors to 128, 64 or even 32. Reduce the the number of colors first, then save the map in 256 colors.The file size will be smaller. You must take into account a discoloration or color cast of your map.