The Coleman (and many/most? other gas stoves) uses the standard screw-on resealable fitting. - lots of brands of gas have this fitting. (e.g. Coleman, Go systems, MSR etc.)
The (resealable cart type) Bleuet uses Camping Gaz's own fitting so need their branded Gas cartridges.Not so common and expensive. Older Bleuet types use the non resealable 'pierced' cartridge - which are cheap and easily available but have to leave on the stove.
My Coleman F1 lite tap seized up irreparably within 6 months. Others have reported the same. Also, the plastic seating for the 3 way pot supports breaks easily. Not a great product IME.
We've had good experience with the Hi Gear Blaze
Has reasonable reviews though I've read a review and heard a from a mate that it is easy to strip the threads if you screw the can on too tightly. It's not happened with us and I guess is due to paranoia over potential leaking gas.
Go outdoors do other good value stoves.
As do Vango (from the same PRC factory as the Hi Gear ones I reckon)
Plenty other heavier value gas stoves which may last a lifetime
(my 1980s Bleuet is still going strong)
Don't dismiss remote cart. gas stoves if you want to use them for actual real cooking...