Virtual Edition, TMSH shows 74gb, web GUI shows 24 gb

74GB is the whole disk. BIG-IP uses Linux Logical Volume Manager (LVM) to create the logical volumes (LVs) for the software (aka boot locations), and shared volumes such as appdata.

You can see the Physical Volume with the "pvs" command. You will see it is approx 74GB.

[admin@bigip:Active:Standalone] ~ # pvs
  PV         VG        Fmt  Attr PSize  PFree
  /dev/sda3  vg-db-vda lvm2 a--  75.79g 9.17g

This is also the size of the one Volume Group ("vgs" command). Note there is some free space, not allocated to any logical volume.

[admin@bigip:Active:Standalone] ~ # vgs
  VG        #PV #LV #SN Attr   VSize  VFree
  vg-db-vda   1  13   0 wz--n- 75.79g 9.17g

Within the volume group are the logical volumes ("lvs" command) which contain the actual filesystems, including the 25GB "appdata" volume:

[admin@bigip:Active:Standalone] ~ # lvs
  LV            VG        Attr       LSize    Pool Origin Data%  Meta%  Move Log Cpy%Sync Convert
  dat.appdata   vg-db-vda -wi-ao----   24.92g
  dat.log       vg-db-vda -wi-ao----    2.93g
  dat.maint.1   vg-db-vda -wi-a-----  300.00m
  dat.share     vg-db-vda -wi-ao----   15.00g
  dat.swapvol   vg-db-vda -wi-ao---- 1000.00m
  set.1._config vg-db-vda -wi-ao----    2.17g
  set.1._usr    vg-db-vda -wi-ao----    5.15g
  set.1._var    vg-db-vda -wi-ao----    3.00g
  set.1.root    vg-db-vda -wi-ao----  440.00m
  set.2._config vg-db-vda -wi-a-----    2.17g
  set.2._usr    vg-db-vda -wi-a-----    5.15g
  set.2._var    vg-db-vda -wi-a-----    4.00g
  set.2.root    vg-db-vda -wi-a-----  440.00m

(Those set.1 and set.2 volumes are the Boot Locations HD1.1, HD1.2.)

The 99% of 24GB disk space shown in Resource Provisioning is the estimated maximum space your modules may grow to need. In theory they should manage themselves to remain under that size. (In practice, in some extreme cases they may not.)

The 19% is how much of the appdata filesystem they are currently using. 19% used is quite healthy, and I would not be worried. You should have logging to look out for logs from diskmonitor should any volume's used space cross thresholds.

See K8865: Overview of the diskmonitor utility

Clearly from the logical volumes above you can see there is lots more space in the 74GB PV to grow. You can use that space for additional Boot Locations (as simply as typing a new number for Volume set name when installing a software image), or if you did need to grow appdata you can do that using "modify /sys disk directory /appdata" tmsh commands. (Note that you can only increase the size, not shrink it, so be sure this is what you want.)

See K14952: Extending disk space on BIG-IP VE