A while back I received a home butcher kit that included a small hand saw. Usually I just bone stuff out but I have used it to cut through some bones in the past. It's never really done a great job and I really didn't use it properly either, at times letting it cut meat as well.
Regardless, it's now kaput and it needs replacement, especially since I really want to start doing bone in cuts. Ideally I'd buy a home band saw designed for the task but that's out of my reach at the moment. So I'm going to have to use a hand saw for the time being.
I guess my real question is this. The blade it originally came with appears to be a simple metal hacksaw blade, is there really that much difference? Or should I look for a specific blade/TPI count?

I like using  sawz all. Mine is electric but plan to get a battery operated.

I do have an old B&D rechargeable reciprocating saw. Use a standard metal blade?

Lem has replacement  meat saw blades.

I use pruning type saw blades in my sawzall. They are super sharp and make quick work of Spine/Pelvis splitting and cutting leg bones. Never used it for bone in cuts though.

I have been using the coarse wood blades.

I don't cut through bones. Marrow can go all over meat. Something to think about.
There's lots of options in bone saws. I've used them for many years doing taxidermy.
One thing to know is they come in dif sizes. Make sure once you order one you either order extra blades or once you order you use correct length.

alliedkenco.com has about everything for meat cutting and packing, sausage seasonings and casings, just about everything you could think of.

Its a whole lot easier if you freeze it first.  You just need to make sure the sawzall is clean and the blade is to.  Then you can just cut rite thru with course bimetal blades [they don't get clogged up as fast] they cut thru bone no problem. One good blade will last all season.  I use the heavy duty ones [I am a carpenter and have them around]
MAP

I rarely cut bone but sometimes split the pelvis and brisket bones if the animal needs to stay at the kill site overnight.  It allows for better cooling.

Anyway, I use a hacksaw with a 12 or 14 TPI blade.  The saw is a regular piece of equipment in the pack.  The cheapest lightest possible is my choice.  The blade is covered with duct tape until needed.

I've had several "bone saws" and none were as good as a hacksaw.