Wild Ben basically said it. The modern load for a 44 Colt uses the .429 bullet, so it will fire in a 44 Mag or 44 Special cylinder. If the overall length is sufficient it will also work in a 44 Special rifle as long as the extractor can get a bite on it.
The cartridge case is 1.06 long, shorter than the 44 special and as stated, the rim is smaller. I shoot 44 Russian in both 44 Colt and 44 Special cylinders, so I never bothered to tool up to reload the 44 Colt. It would be one more look-alike case to sort, and the 44 Russian is easier to spot in a pile of brass.
Some 44 Colt chambered cylinders will not accept 44 Russian or shortened 44 Special as the rim recess might be too small, but most cylinders will take the larger rim.