Don't know what your old bike is but MTB "Type" bikes are normally measured in inches and road/ comfort/ hybrids in Cms. You can convert inches to Cms as you have done and come up with the seat tube length.---But there is a difference between MTB and Road bikes in other dimensions. The top tube on an MTB (Size for size) is longer. although both frames are sold in Seat tube length- it is the top tube length that denotes how well a frame will fit you.

So your old 18" frame that fits you is a 46cm. So you would think that a 50cm road bike would make for a bigger fit- but it doesn't.

Looking at the Giant Specs and geometry--An 18" MTB Frame (46 cms) will have a top tube length of 23.4"- That equates to TT in metric of 594mm.

The road bike of 46.5cms has a top tube length of 530mm.

Perhaps it would be better if the two types of bike were both measured in the same scale but I think it would cause problems. I ride a 51 cm road frame. If I were to get an MTB frame in that size- I might be stretching for the bars a bit. Hence I ride a 15" MTB Frame instead of the 20" that 51cm equates to in Seat tube

Now if you just ride an odd sized road bike- then all the above is rubbish so disregard it.

Attached are my MTB and My main Road ride. Both fit me and I would not like to ride either bike in a different size.