Multiflora does not send out shoots. It seeds around, but that is different. Also, roses with multiflora heritage all have the fringed multiflora stipules. This would be polyanthas, hybrid musks, and multiflora ramblers, just to name a few.

Primula and hugonis do look somewhat different. However, my own-root hugonis has been extremely slow to develop suckers. Given that, it shouldn't be difficult to tell the difference between a planted rose and a seedling.

Yes, the foliage, the canes color and the thorns are are all obviously different. If you see hugonis or primula leaves and canes just once, you will never mix them with multiflora.
Olga