I am reading David Tong's lectures on string theory and on the page 180 in chapter 7 of his lecture notes http://www.damtp.cam.ac.uk/user/tong/string.html : he claims that D-branes are something in between the fundamental strings, which tension is independent of $g_s$, and solitonic branes, whose tension scales as $1/g_s^2$. And he says then, that there is some analogue to D-brane in field theory, despite not so frequently mentioned. What does he actually mean?
Absolutely! Even if someone rejects string theory, D-branes are still a very useful and geometrical ways to construct (and predict!) a plethora of new objects in QFT. Everthing from perturbativate states like fermions, mesons, baryons to everthing non-perturbative like instantons, monopoles, dyons, votices, kinks, textures, condensates, cosmic strings, brane worlds, superconductors, non-trivial phases of matter, domain walls (and all its noncommutative counterparts) etc. can be engeeniered from brane configurations. In string theory, every object is a soliton (perhaps by changing the duality frame).
Almost any kind of solition you can immagine is analogous to a D-brane configuration (even gravitational ones!). I recommend you to read Tong's lectures: https://www.damtp.cam.ac.uk/user/tong/tasi/tasi.pdf