I'd definitely say it's a Smith & Wesson of some sort, but I don't think it's a model 10. But they do so many varieties, and their stuff gets modified so much, that I can't tell for sure what model it is. The cylinder release thumb switch below the hammer is pretty much a dead giveaway- if it's not a true S&W, it's a knockoff. And by the size of it, especially the taper on that barrel, it looks more like a .32 than a .38 to me.
Probably either a 'detective special' or a modified pocket pistol for concealed carry if I had to guess. Possibly either a Model 30 or a knockoff.
Not a pistol expert, but I did carry a S&W Model 10 in .38 Special for seven years, and spent a lot of time shooting and servicing it. Not identical, but a lot of very similar features on it.
It might also be a cheap no-name one, which is why it seems to include a few features that almost look more Colt than S&W. I have an old .32 pistol from around the turn of the century that is a bad S&W knockoff, and lmost looks like it was made by someone from memory instead with an actual example to copy. This has a similar feel to it.
