What is the difference between a strong acid and a weak acid as well as a strong base versus a weak base with regards to ionization?

Hint :The Bronsted–Lowry theory, also known as the proton theory of acids and bases, is a theory proposed by the Danish chemist Johannes Nicolaus Brnsted and the English chemist Thomas Martin Lowry in 1923. It states that any compound that can transfer a proton to another compound is an acid, and any compound that accepts the proton is a base.

Complete Step By Step Answer:
To understand the difference between a strong acid and a weak acid as well as a strong base versus a weak base with regards to ionization Let's look at the Bronsted-Lowry concept of acids and bases. It states that:
${H^ + }ions$are donated to an aqueous solution if it’s an acid
${H^ + }ions$are accepted in an aqueous solution if it’s a base
In an aqueous solution, strong acids like $HCl$will almost completely dissociate, or ionise, into ions:
$HCl(aq) \to {H^ + }(aq) + C{l^ - }(aq)$
Weak acids, such as acetic acid ( $C{H_3}COOH$ ), do not ionise to the same degree as strong acids, but they do ionise to some extent, and this reaction occurs:$C{H_3}COOH(aq) \rightleftharpoons {H^ + }(aq) + C{H_3}CO{O^ - }(aq)$
In an aqueous solution, strong bases like $NaOH$ can essentially totally ionize, or dissociate, into ions.$NaOH(aq) \to O{H^ - }(aq) + N{a^ + }(aq)$
Weak bases, like $N{H_3}$, like weak acids, can dissociate just very slightly in an aqueous solution. The reaction described below will occur, but it will be uncommon.$N{H_3}(aq) \rightleftharpoons O{H^ - }(aq) + NH_4^ + (aq)$

Note :
A material can only act as an acid in the presence of a base, and a substance can only function as a base in the presence of an acid, according to the Bronsted–Lowry system. Furthermore, when an acidic substance lacks a proton, it forms a base known as an acid's conjugate base, and when a basic substance gains a proton, it forms an acid known as a base's conjugate acid.