The reality is that there are so many ways for getting brown and red/brown tones that, especially with a digitally copied image viewed on different monitors, guessing which process was used is something of a lottery.
The first looks like POP or copper toning. Copper can give anything in the range from cold brown to warm brown, orange, bright pink and many in-between. Gold after sepia or polysulphide can give from subtle warming up to strong reds or salmon colours. Partial gold on sepia gives many in-between hues too.
The second looks like simple sepia, which can also produce a huge range of colours, depending on the paper, the toner mix and also on the bleach - and whether duotoned with seleniium for example. It could be a lith print though - these can give colours like this and although they can be graphic they can also be very gentle and subtle - or a mixture of the two, which is why it is such an expressive printing technique. I would guess it is sepia (eg thiourea) though, but wouldn't put money on it!.
There are other brown and red/brown techniques too, so take your choice!

Tim