  We consider two balayage constructions on the complex plane $\mathbb C$ with
real axis $\mathbb R$ for $0\leq b\in \mathbb R$. Let $u\not\equiv -\infty$ be
a subharmonic function on $\mathbb C$ of order
$$\operatorname{ord}[u]:=\limsup_{z\to \infty} \frac{\ln \max\{1,u(z)\}}{\ln
|z|}\leq 1,$$ $U=u-v$ be the difference of subharmonic functions $u$ and
$v\not\equiv -\infty$ on $\mathbb C$ with $\operatorname{ord}[v]\leq 1$, i.e.,
$\delta$-subharmonic function on $\mathbb C$ of order
$\operatorname{ord}[U]\leq 1$. Then there is a $\delta$-subharmonic function
$V\not\equiv \pm\infty$ on $\mathbb C$ of order $\operatorname{ord}[V]\leq 1$
such that $V$ is harmonic on $\bigl\{ z \in \mathbb C\bigm| |\Re z|> b\bigr\}$
and $U(z)\equiv V(z)$ for all $z\in \bigl\{ z \in \mathbb C\bigm| |\Re z|\leq
b\bigr\}\setminus E$ where $E\subset \mathbb C$ is polar.
  If $u$ is a subharmonic function of finite type under order $1$, i.e.,
$$\limsup_{z\to \infty} \frac{u(z)}{|z|}<+\infty,$$ then there exist
subharmonic functions $u_{\mathbb R}$ and $u_b$ of finite type under order $1$
that are harmonic respectively on $\mathbb C\setminus \mathbb R$ and $\bigl\{ z
\in \mathbb C\bigm| |\Re z|> b\bigr\}$ such that $$\begin{cases} u(z)\equiv
u_{\mathbb R}(z)+u_b(z) \text{ for all $z\in {\mathbb R}\bigcup \bigl\{ z \in
\mathbb C\bigm| |\Re z|\leq b\bigr\}$},\\ u(z)\leq u_{\mathbb R}(z) + u_b(z)
\text{ for each $z\in \mathbb C$.}\end{cases}$$ At the same time, we trace
special relationships between the various logarithmic characteristics of the
Riesz mass and charge distributions of subharmonic and $\delta$-subharmonic
functions.
