"Speculative thinking" has two main senses in modern philosophy, one from Kant, the other from Hegel.
Kant uses the expression "speculative thinking" in a negative sense. It is the metaphysical thinking that pretends to know facts beyond the realm of possible experience. He refers by it to the likes of Descartes, Spinoza, Leibniz.
A cursory view of the present work will lead to the supposition that its use is merely negative, that it only serves to warn us against venturing, with speculative reason, beyond the limits of experience. This is, in fact, its primary use. (Critique of Pure Reason Preface to the Second Edition)
Hegel uses the expression "speculative thinking" in a positive sense. It is the kind of thinking that he supposedly exemplifies in his own work, a thinking that bridges all the gaps until every item is necessarily connected and explained.
The method of empirical science exhibits two defects. The first is that the Universal . . . not on its own account connected with the Particulars or the details. Either is external and accidental to the other; and it is the same with the particular facts which are brought into union: each is external and accidental to the others. The second defect is that the beginnings are in every case data and postulates, neither accounted for nor deduced. In both these points the form of necessity fails to get its due. Hence reflection, whenever it sets itself to remedy these defects, becomes speculative thinking, the thinking proper to philosophy. (Shorter Logic § 9)
"Speculative Realism" seems to be a kind of late reaction against Kant. It uses "speculative" in Kant's sense (overstepping the limits of possible experience) but with an opposite, positive evaluation. It is a kind of return to pre Kantian metaphysics.