Distinction of Dirac monopole and Polyakov-'t Hooft monopole Can anybody explain the physical difference between Dirac monopole and Polyakov monopole? 
First, let me write down what I know briefly. 
Dirac monopole


*

*It comes from the symmetry of Maxwell equation. By assuming that magnetic field for a point source magnetic charge $g$. 


\begin{align}
B(r,t) = \frac{g}{4\pi r^2} \frac{\vec{r}}{r}
\end{align}
Since the divergence of $B$ gives non-vanishing value due to delta function $\nabla \cdot \nabla(\frac{1}{r})=\delta(r)$. Thus we introduce the so-called Dirac String, ($i.e$, add some solenoid field)


*Dirac string is non-obeservable due to Dirac's charge quantization



Polyakov-'t Hooft  monopole. 


*

*It comes from soliton Dynamics. $i.e$ $SO(3)$ model

*We can compute the mass (Energy)

*For large distance Polyakov-'t Hooft  monopole behaves like Dirac monopole

You can comment anything including above things.
This question arise from the comment of my previous question [Compact QED and Non-compact QED - Polyakov textbook ] by Stephen Powell
 A: *

*A (generalized) 't Hooft-Polyakov monopole and

*a Dirac monopole with a Dirac string attached
are two types of magnetic monopoles, which differ in several ways, as OP and user ACuriousMind correctly state.


*

*On one hand, a (generalized) 't Hooft-Polyakov monopole is a regular, soliton-like, finite-energy solution to the classical Euler-Lagrange field equations of some GUT (with an action principle that extends the standard model). Its existence is unavoidable if a certain topological condition is satisfied in the GUT.

*On the other hand, while Dirac monopoles were mostly conceived by Dirac as a theoretical laboratory to study charge quantization, the modern interpretation is that a Dirac monopole is an effective description far away from the monopole that fails near the finite core region of the monopole. Moreover a Dirac monopole requires a non-standard action principle, cf. e.g. this Phys.SE post and links therein.
For further differences and details, see Ref. 1 and the linked Wikipedia pages.
References: 


*

*F.A. Bais, To be or not to be? Magnetic monopoles in non-abelian gauge theories, arXiv:hep-th/0407197. (Hat tip: Hunter.)

