They are quite different.
Inductive thinking is usually considered in opposition to deductive thinking; those are forms of thinking that we all apply, according to the situation. Inductive thinking means essentially to create a rule starting from multiple specific cases; deductive thinking is the opposite: to apply a rule to a specific case.
If you see a person running, you might think she has a problem. But if you see another and then another, and then another running, all in the same direction, you will deduce all of them are following the same behavior. That's deductive thinking. A rule has been developed from multiple observations: people is probably is escaping from some risk. Now, you will apply the rule to yourself: if people escape from some danger, and I am part of the people, I should do the same thing. That's inductive thinking.
On the other hand, convergent thinking is considered in opposition to divergent thinking. Those are not related to a rule. Those forms of thinking are related to specific ways that problems are solved. Convergent thinking means solving a problem by following standard knowledge, standard rules. Divergent thinking is to solve a problem in creative forms.
For example, in order to multiply any number, say 5500, times 9, you can write down the calculation, as we've learnt in school. That's convergent thinking: you've followed the standard way of solving such problem. But you can do it in a different way: multiply it by 10 (55000) and then remove it once (-5500), which gives 49500. A simple, non-standard but useful solution, that might even be faster. I bet you can come up with more creative solutions which others might not imagine (e.g. 5000x9 + 500x9). That's divergent thinking.