The contacts of any fuse, especially if it has silver caps, should never be touched with your fingers! That's easier said than done, how could you place or remove a fuse without damaging a PCB fuse holder or the fuse itself and without touching any part of the fuse caps during the installation? Without these special fuse tweezers that's nearly impossible indeed. Over the years, we've seen many damaged PCBs, fuse holders and fuses. Touching caps with "sweaty" or otherwise dirty fingers leaves an acidous residue onto the caps, leading to oxidation and thus to an increase of contact resistance, in addition to this, prying with hard objects like screwdrivers easily leads to damaging of the fuse. All this can be avoided by using these simple tools.
Note: both sizes are dedicated to that size only. You cannot use one size of tweezers for both fuse sizes.