Hi Kristopher,
Assuming this is on Linux / Unix, this value is determined by looking at how many entries there are in the /proc/<PID>/fd directory, where PID is the process ID of the Node Exporter. Note that the "process_xxx" metrics are default metrics included by the Prometheus Go client library about the exporting process itself (so in your case, about the Node Exporter), and not about the machine. When I compare the number of entries in /proc/<PID>/fd, I do see three additional descriptors in lsof that are not listed in that directory, which are the binary itself, and the directory the binary is contained in, and the root directory. So maybe that difference in accounting is where your discrepancy comes from?
$ lsof -c node_exporter
COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME
node_expo 13943 julius cwd DIR 8,18 4096 7999933 /XXXXXXXX/prometheus/node_exporter
node_expo 13943 julius rtd DIR 8,18 4096 2 /
node_expo 13943 julius txt REG 8,18 19027879 4989900 /XXXXXXXX/prometheus/node_exporter/node_exporter
node_expo 13943 julius 0u CHR 136,1 0t0 4 /dev/pts/1
node_expo 13943 julius 1u CHR 136,1 0t0 4 /dev/pts/1
node_expo 13943 julius 2u CHR 136,1 0t0 4 /dev/pts/1
node_expo 13943 julius 3u IPv6 98870 0t0 TCP *:9100 (LISTEN)
node_expo 13943 julius 4u a_inode 0,13 0 12663 [eventpoll]
node_expo 13943 julius 5r FIFO 0,12 0t0 98866 pipe
node_expo 13943 julius 6w FIFO 0,12 0t0 98866 pipe
node_expo 13943 julius 7u IPv6 99715 0t0 TCP ip6-localhost:9100->ip6-localhost:44322 (ESTABLISHED)
$ l /proc/13943/fd
total 0
dr-x------ 2 julius julius 0 Feb 10 12:37 ./
dr-xr-xr-x 9 julius julius 0 Feb 10 12:37 ../
lrwx------ 1 julius julius 64 Feb 10 12:37 0 -> /dev/pts/1
lrwx------ 1 julius julius 64 Feb 10 12:37 1 -> /dev/pts/1
lrwx------ 1 julius julius 64 Feb 10 12:37 2 -> /dev/pts/1
lrwx------ 1 julius julius 64 Feb 10 12:37 3 -> 'socket:[98870]'
lrwx------ 1 julius julius 64 Feb 10 12:37 4 -> 'anon_inode:[eventpoll]'
lr-x------ 1 julius julius 64 Feb 10 12:37 5 -> 'pipe:[98866]'
l-wx------ 1 julius julius 64 Feb 10 12:37 6 -> 'pipe:[98866]'
lrwx------ 1 julius julius 64 Feb 10 12:37 7 -> 'socket:[99715]'
Regards,
Julius